Palindromic subshifts and simple periodic groups of intermediate growth

Abstract

We describe a new class of groups of Burnside type, by giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group. We show that if the associated Schreier graphs are linearly repetitive, then the group is of intermediate growth. In particular, this gives first examples of simple groups of intermediate growth.

  • [amirangelvirag:linear] Go to document G. Amir, O. Angel, and B. Virág, "Amenability of linear-activity automaton groups," J. Eur. Math. Soc. (JEMS), vol. 15, iss. 3, pp. 705-730, 2013.
    @ARTICLE{amirangelvirag:linear,
      author = {Amir, Gideon and Angel, Omer and Virág, Bálint},
      title = {Amenability of linear-activity automaton groups},
      journal = {J. Eur. Math. Soc. (JEMS)},
      fjournal = {Journal of the European Mathematical Society (JEMS)},
      volume = {15},
      year = {2013},
      number = {3},
      pages = {705--730},
      issn = {1435-9855},
      mrclass = {43A07 (20E08 20P05 60J05)},
      mrnumber = {3085088},
      mrreviewer = {Wolfgang Woess},
      doi = {10.4171/JEMS/373},
      zblnumber = {1277.37019},
      }
  • [adian:book] S. I. Adian, The Burnside Problem and Identities in Groups, Springer-Verlag, New York, 1979, vol. 95.
    @BOOK{adian:book,
      author = {Adian, S. I.},
      title = {The {B}urnside Problem and Identities in Groups},
      series = {Ergeb. Math. Grenzgeb.},
      volume = {95},
      note = {translated from the Russian by John Lennox and James Wiegold},
      publisher = {Springer-Verlag, New York},
      year = {1979},
      pages = {xi+311},
      isbn = {3-540-08728-1},
      mrclass = {20F05},
      mrnumber = {0537580},
      zblnumber = {},
      }
  • [adyan:randomwalk] Go to document S. I. Adyan, "Random walks on free periodic groups," Izv. Akad. Nauk SSSR Ser. Mat., vol. 46, iss. 6, pp. 1139-1149, 1343, 1982.
    @ARTICLE{adyan:randomwalk,
      author = {Adyan, S. I.},
      title = {Random walks on free periodic groups},
      journal = {Izv. Akad. Nauk SSSR Ser. Mat.},
      fjournal = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
      volume = {46},
      year = {1982},
      number = {6},
      pages = {1139--1149, 1343},
      issn = {0373-2436},
      mrclass = {43A07 (20F50 60B15 60J15)},
      mrnumber = {0682486},
      mrreviewer = {P. Gerl},
      zblnumber = {0512.60012},
      doi = {10.1070/IM1983v021n03ABEH001799},
      }
  • [al:burn_en] S. V. Alevsin, "Finite automata and the Burnside problem for periodic groups," Mat. Zametki, vol. 11, pp. 319-328, 1972.
    @ARTICLE{al:burn_en,
      author = {Ale{š}in, S. V.},
      title = {Finite automata and the {B}urnside problem for periodic groups},
      journal = {Mat. Zametki},
      fjournal = {Akademiya Nauk SSSR. Matematicheskie Zametki},
      volume = {11},
      year = {1972},
      pages = {319--328},
      issn = {0025-567X},
      mrclass = {20F50 (94A30)},
      mrnumber = {0301107},
      mrreviewer = {Heinrich Seidel},
      zblnumber = {0246.20024},
      }
  • [allouchshallit:sequences] Go to document J. Allouche and J. Shallit, Automatic Sequences. Theory, Applications, Generalizations, Cambridge University Press, Cambridge, 2003.
    @BOOK{allouchshallit:sequences,
      author = {Allouche, Jean-Paul and Shallit, Jeffrey},
      title = {Automatic Sequences. Theory, Applications, Generalizations},
      publisher = {Cambridge University Press, Cambridge},
      year = {2003},
      pages = {xvi+571},
      isbn = {0-521-82332-3},
      mrclass = {11B85 (11Z05 37A45 37B10 68Q45 68R15 94A45)},
      mrnumber = {1997038},
      mrreviewer = {Valérie Berthé},
      doi = {10.1017/CBO9780511546563},
      zblnumber = {1086.11015},
      }
  • [barth:growthsurvey] Go to document L. Bartholdi, "Growth of groups and wreath products," in Groups, Graphs and Random Walks, Cambridge Univ. Press, Cambridge, 2017, vol. 436, pp. 1-76.
    @INCOLLECTION{barth:growthsurvey,
      author = {Bartholdi, Laurent},
      title = {Growth of groups and wreath products},
      booktitle = {Groups, Graphs and Random Walks},
      series = {London Math. Soc. Lecture Note Ser.},
      volume = {436},
      pages = {1--76},
      publisher = {Cambridge Univ. Press, Cambridge},
      year = {2017},
      mrclass = {20-02 (20E07 20E22)},
      mrnumber = {3644003},
      zblnumber = {1373.20054},
      doi = {10.1017/9781316576571},
      }
  • [BE:permextensions] Go to document L. Bartholdi and A. Erschler, "Growth of permutational extensions," Invent. Math., vol. 189, iss. 2, pp. 431-455, 2012.
    @ARTICLE{BE:permextensions,
      author = {Bartholdi, Laurent and Erschler, Anna},
      title = {Growth of permutational extensions},
      journal = {Invent. Math.},
      fjournal = {Inventiones Mathematicae},
      volume = {189},
      year = {2012},
      number = {2},
      pages = {431--455},
      issn = {0020-9910},
      mrclass = {20E22 (20F05)},
      mrnumber = {2947548},
      mrreviewer = {Matthew B. Day},
      doi = {10.1007/s00222-011-0368-x},
      zblnumber = {1286.20025},
      }
  • [BE:givengrowth] Go to document L. Bartholdi and A. Erschler, "Groups of given intermediate word growth," Ann. Inst. Fourier (Grenoble), vol. 64, iss. 5, pp. 2003-2036, 2014.
    @ARTICLE{BE:givengrowth,
      author = {Bartholdi, Laurent and Erschler, Anna},
      title = {Groups of given intermediate word growth},
      journal = {Ann. Inst. Fourier (Grenoble)},
      fjournal = {Université de Grenoble. Annales de l'Institut Fourier},
      volume = {64},
      year = {2014},
      number = {5},
      pages = {2003--2036},
      issn = {0373-0956},
      mrclass = {20F05 (20F65)},
      mrnumber = {3330929},
      mrreviewer = {Varujan Atabekyan},
      doi = {10.5802/aif.2902},
      zblnumber = {1317.20043},
      }
  • [bartholdiErschler:imbeddings] Go to document L. Bartholdi and A. Erschler, "Imbeddings into groups of intermediate growth," Groups Geom. Dyn., vol. 8, iss. 3, pp. 605-620, 2014.
    @ARTICLE{bartholdiErschler:imbeddings,
      author = {Bartholdi, Laurent and Erschler, Anna},
      title = {Imbeddings into groups of intermediate growth},
      journal = {Groups Geom. Dyn.},
      fjournal = {Groups, Geometry, and Dynamics},
      volume = {8},
      year = {2014},
      number = {3},
      pages = {605--620},
      issn = {1661-7207},
      mrclass = {20F05 (20F69 46B85)},
      mrnumber = {3267517},
      mrreviewer = {Yago Antol\'\i n},
      doi = {10.4171/GGD/241},
      zblnumber = {1335.20046},
      }
  • [baakegrimm] Go to document M. Baake and U. Grimm, Aperiodic Order. Vol. 1. A Mathematical Invitation, Cambridge University Press, Cambridge, 2013, vol. 149.
    @BOOK{baakegrimm,
      author = {Baake, Michael and Grimm, Uwe},
      title = {Aperiodic {O}rder. {V}ol. 1. {A} {M}athematical {I}nvitation},
      series = {Encyclopedia Math. Appl.},
      volume = {149},
      note = {with a foreword by Roger Penrose},
      publisher = {Cambridge University Press, Cambridge},
      year = {2013},
      pages = {xvi+531},
      isbn = {978-0-521-86991-1},
      mrclass = {52C23 (11H06 20C35 20H15 82D25)},
      mrnumber = {3136260},
      mrreviewer = {Jean-Pierre Gazeau},
      doi = {10.1017/CBO9781139025256},
      zblnumber = {1295.37001},
      }
  • [handbook:branch] Go to document L. Bartholdi, R. I. Grigorchuk, and Z. vSuni’k, "Branch groups," in Handbook of Algebra, Vol. 3, North-Holland, Amsterdam, 2003, pp. 989-1112.
    @INCOLLECTION{handbook:branch,
      author = {Bartholdi, Laurent and Grigorchuk, Rostislav I. and {Š}uni{\'k},
      Zoran},
      title = {Branch groups},
      booktitle = {Handbook of Algebra, Vol. 3},
      publisher = {North-Holland, Amsterdam},
      year = {2003},
      pages = {989--1112},
      zblnumber = {1140.20306},
      doi = {10.1016/S1570-7954(03)80078-5},
      mrnumber = {2035113},
     }
  • [bkn:amenability] Go to document L. Bartholdi, V. A. Kaimanovich, and V. V. Nekrashevych, "On amenability of automata groups," Duke Math. J., vol. 154, iss. 3, pp. 575-598, 2010.
    @ARTICLE{bkn:amenability,
      author = {Bartholdi, Laurent and Kaimanovich, Vadim A. and Nekrashevych, Volodymyr V.},
      title = {On amenability of automata groups},
      journal = {Duke Math. J.},
      fjournal = {Duke Mathematical Journal},
      volume = {154},
      year = {2010},
      number = {3},
      pages = {575--598},
      issn = {0012-7094},
      mrclass = {20E08 (20P05 43A07 60G50)},
      mrnumber = {2730578},
      mrreviewer = {Yair Glasner},
      doi = {10.1215/00127094-2010-046},
      zblnumber = {1268.20026},
      }
  • [bajorskamacedonska] Go to document B. Bajorska and O. Macedońska, "A note on groups of intermediate growth," Comm. Algebra, vol. 35, iss. 12, pp. 4112-4115, 2007.
    @ARTICLE{bajorskamacedonska,
      author = {Bajorska, B. and Macedońska, O.},
      title = {A note on groups of intermediate growth},
      journal = {Comm. Algebra},
      fjournal = {Communications in Algebra},
      volume = {35},
      year = {2007},
      number = {12},
      pages = {4112--4115},
      issn = {0092-7872},
      mrclass = {20E26 (20E07)},
      mrnumber = {2372323},
      mrreviewer = {Goulnara N. Arzhantseva},
      doi = {10.1080/00927870701544914},
      zblnumber = {1132.20016},
      }
  • [bezuglyiMedynets:fullgroup] Go to document S. Bezuglyi and K. Medynets, "Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems," Colloq. Math., vol. 110, iss. 2, pp. 409-429, 2008.
    @ARTICLE{bezuglyiMedynets:fullgroup,
      author = {Bezuglyi, S. and Medynets, K.},
      title = {Full groups, flip conjugacy, and orbit equivalence of {C}antor minimal systems},
      journal = {Colloq. Math.},
      fjournal = {Colloquium Mathematicum},
      volume = {110},
      year = {2008},
      number = {2},
      pages = {409--429},
      issn = {0010-1354},
      mrclass = {37B05 (20B99 28A60 28D05 37A20)},
      mrnumber = {2353913},
      mrreviewer = {Jan Kwiatkowski},
      doi = {10.4064/cm110-2-6},
      zblnumber = {1142.37011},
      }
  • [boshernitzan:linearrep] Go to document M. D. Boshernitzan, "A condition for unique ergodicity of minimal symbolic flows," Ergodic Theory Dynam. Systems, vol. 12, iss. 3, pp. 425-428, 1992.
    @ARTICLE{boshernitzan:linearrep,
      author = {Boshernitzan, Michael D.},
      title = {A condition for unique ergodicity of minimal symbolic flows},
      journal = {Ergodic Theory Dynam. Systems},
      fjournal = {Ergodic Theory and Dynamical Systems},
      volume = {12},
      year = {1992},
      number = {3},
      pages = {425--428},
      issn = {0143-3857},
      mrclass = {58F03 (28D05 58F11)},
      mrnumber = {1182655},
      mrreviewer = {Mariusz Lemańczyk},
      doi = {10.1017/S0143385700006866},
      zblnumber = {0756.58030},
      }
  • [buxperez:imgi] Go to document K. Bux and R. Pérez, "On the growth of iterated monodromy groups," in Topological and Asymptotic Aspects of Group Theory, Amer. Math. Soc., Providence, RI, 2006, vol. 394, pp. 61-76.
    @INCOLLECTION{buxperez:imgi,
      author = {Bux, Kai-Uwe and Pérez, Rodrigo},
      title = {On the growth of iterated monodromy groups},
      booktitle = {Topological and Asymptotic Aspects of Group Theory},
      series = {Contemp. Math.},
      volume = {394},
      pages = {61--76},
      publisher = {Amer. Math. Soc., Providence, RI},
      year = {2006},
      mrclass = {20F65 (20E08 37F20 37F50)},
      mrnumber = {2216706},
      mrreviewer = {Laurent Bartholdi},
      doi = {10.1090/conm/394/07434},
      zblnumber = {1103.20038},
      }
  • [brieussel] Go to document J. Brieussel, "Growth behaviors in the range $e^{r^\alpha}$," Afr. Mat., vol. 25, iss. 4, pp. 1143-1163, 2014.
    @ARTICLE{brieussel,
      author = {Brieussel, Jérémie},
      title = {Growth behaviors in the range {$e^{r^\alpha}$}},
      journal = {Afr. Mat.},
      fjournal = {Afrika Matematika},
      volume = {25},
      year = {2014},
      number = {4},
      pages = {1143--1163},
      issn = {1012-9405},
      mrclass = {20F65 (05E18 20E08 26A12)},
      mrnumber = {3277875},
      mrreviewer = {Dmytro M. Savchuk},
      doi = {10.1007/s13370-013-0182-2},
      zblnumber = {1337.20041},
      }
  • [barthsunik] L. Bartholdi and Z. vSuni’k, "On the word and period growth of some groups of tree automorphisms," Comm. Algebra, vol. 29, iss. 11, pp. 4923-4964, 2001.
    @ARTICLE{barthsunik,
      author = {Bartholdi, Laurent and {Š}uni{\'k},
      Zoran},
      title = {On the word and period growth of some groups of tree automorphisms},
      journal = {Comm. Algebra},
      volume = {29},
      year = {2001},
      number = {11},
      pages = {4923--4964},
      zblnumber = {1001.20027},
      mrnumber = {1856923},
      }
  • [burnside:problem] W. Burnside, "On an unsettled question in the theory of discontinuous groups," Quart. J. Pure Appl. Math., vol. 33, pp. 230-238, 1902.
    @ARTICLE{burnside:problem,
      author = {Burnside, W.},
      title = {On an unsettled question in the theory of discontinuous groups},
      journal = {Quart. J. Pure Appl. Math.},
      volume = {33},
      year = {1902},
      pages = {230--238},
      zblnumber = {33.0149.01},
      }
  • [barthvirag] Go to document L. Bartholdi and B. Virág, "Amenability via random walks," Duke Math. J., vol. 130, iss. 1, pp. 39-56, 2005.
    @ARTICLE{barthvirag,
      author = {Bartholdi, Laurent and Virág, Bálint},
      title = {Amenability via random walks},
      journal = {Duke Math. J.},
      fjournal = {Duke Mathematical Journal},
      volume = {130},
      year = {2005},
      number = {1},
      pages = {39--56},
      issn = {0012-7094},
      mrclass = {43A07 (20P05 60G50)},
      mrnumber = {2176547},
      mrreviewer = {Vydas {\v{C}}ekanavi{\v{c}}ius},
      doi = {10.1215/S0012-7094-05-13012-5},
      zblnumber = {1104.43002},
      }
  • [chou:elementaryamenable] Go to document C. Chou, "Elementary amenable groups," Illinois J. Math., vol. 24, iss. 3, pp. 396-407, 1980.
    @ARTICLE{chou:elementaryamenable,
      author = {Chou, Ching},
      title = {Elementary amenable groups},
      journal = {Illinois J. Math.},
      fjournal = {Illinois Journal of Mathematics},
      volume = {24},
      year = {1980},
      number = {3},
      pages = {396--407},
      issn = {0019-2082},
      mrclass = {43A07 (20E99)},
      mrnumber = {0573475},
      mrreviewer = {J. Wiegold},
      url = {http://projecteuclid.org/euclid.ijm/1256047608},
      zblnumber = {0439.20017},
      }
  • [ChJN] M. Chornyi, K. Juschenko, and V. Nekrashevych, On topological full groups of $\mathbb{Z}^d$-actions, 2016.
    @MISC{ChJN,
      author = {Chornyi, M. and Juschenko, K. and Nekrashevych, V.},
      title = {On topological full groups of $\mathbb{Z}^d$-actions},
      arxiv = {1602.04255},
      year = {2016},
      zblnumber = {},
      }
  • [cornulier:pleinstopologiques] Y. de Cornulier, "Groupes pleins-topologiques (d’après Matui, Juschenko, Monod, $\ldots$)," Astérisque, iss. 361, p. exp. no. 1064, viii, 183-223, 2014.
    @ARTICLE{cornulier:pleinstopologiques,
      author = {de Cornulier, Yves},
      title = {Groupes pleins-topologiques (d'après {M}atui, {J}uschenko, {M}onod, {$\ldots$})},
      journal = {Astérisque},
      fjournal = {Astérisque},
      number = {361},
      year = {2014},
      pages = {Exp. No. 1064, viii, 183--223},
      issn = {0303-1179},
      isbn = {978-285629-785-8},
      mrclass = {37B05 (54H11)},
      mrnumber = {3289281},
      mrreviewer = {Rémi Boutonnet},
      zblnumber = {1365.54001},
      }
  • [damaniklenz] Go to document D. Damanik and D. Lenz, "Substitution dynamical systems: characterization of linear repetitivity and applications," J. Math. Anal. Appl., vol. 321, iss. 2, pp. 766-780, 2006.
    @ARTICLE{damaniklenz,
      author = {Damanik, David and Lenz, Daniel},
      title = {Substitution dynamical systems: characterization of linear repetitivity and applications},
      journal = {J. Math. Anal. Appl.},
      fjournal = {Journal of Mathematical Analysis and Applications},
      volume = {321},
      year = {2006},
      number = {2},
      pages = {766--780},
      issn = {0022-247X},
      mrclass = {37B10 (37A20 37A25 39A70 47B36 47B80 81Q10 82D25)},
      mrnumber = {2241154},
      mrreviewer = {César R. de Oliveira},
      doi = {10.1016/j.jmaa.2005.09.004},
      zblnumber = {1094.37007},
      }
  • [erschler:nonresfin] Go to document A. Erschler, "Not residually finite groups of intermediate growth, commensurability and non-geometricity," J. Algebra, vol. 272, iss. 1, pp. 154-172, 2004.
    @ARTICLE{erschler:nonresfin,
      author = {Erschler, Anna},
      title = {Not residually finite groups of intermediate growth, commensurability and non-geometricity},
      journal = {J. Algebra},
      fjournal = {Journal of Algebra},
      volume = {272},
      year = {2004},
      number = {1},
      pages = {154--172},
      issn = {0021-8693},
      mrclass = {20F05 (20F50 20F65)},
      mrnumber = {2029029},
      mrreviewer = {Stephen P. Humphries},
      doi = {10.1016/j.jalgebra.2002.11.005},
      zblnumber = {1049.20019},
      }
  • [erschler:piecwise] Go to document A. Erschler, "Piecewise automatic groups," Duke Math. J., vol. 134, iss. 3, pp. 591-613, 2006.
    @ARTICLE{erschler:piecwise,
      author = {Erschler, Anna},
      title = {Piecewise automatic groups},
      journal = {Duke Math. J.},
      fjournal = {Duke Mathematical Journal},
      volume = {134},
      year = {2006},
      number = {3},
      pages = {591--613},
      issn = {0012-7094},
      mrclass = {20F65 (20F69 43A07 57M07)},
      mrnumber = {2254627},
      mrreviewer = {Tullio G. Ceccherini-Silberstein},
      doi = {10.1215/S0012-7094-06-13435-X},
      zblnumber = {1159.20019},
      }
  • [ershov:gs] Go to document M. Ershov, "Kazhdan quotients of Golod-Shafarevich groups," Proc. Lond. Math. Soc. (3), vol. 102, iss. 4, pp. 599-636, 2011.
    @ARTICLE{ershov:gs,
      author = {Ershov, Mikhail},
      title = {Kazhdan quotients of {G}olod-{S}hafarevich groups},
      journal = {Proc. Lond. Math. Soc. (3)},
      fjournal = {Proceedings of the London Mathematical Society. Third Series},
      volume = {102},
      year = {2011},
      number = {4},
      pages = {599--636},
      issn = {0024-6115},
      mrclass = {20E18 (20F05 20F69 22D10 43A07)},
      mrnumber = {2793445},
      mrreviewer = {Javier Otal},
      doi = {10.1112/plms/pdq022},
      zblnumber = {1280.20037},
      }
  • [grigorchlysenok:burnside] Go to document R. Grigorchuk and I. Lysenok, "The Burnside problems," in The Concise Handbook of Algebra, Kluwer Academic Publishers, Dordrecht, 2002, pp. 111-115.
    @INCOLLECTION{grigorchlysenok:burnside,
      author = {Grigorchuk, Rostislav and Lysenok, I.},
      title = {The {Burnside} problems},
      booktitle = {The Concise Handbook of Algebra},
      note = {Alexander~V. Mikhalev and G{ü}nter~F. Pilz, eds.},
      publisher = {Kluwer Academic Publishers, Dordrecht},
      year = {2002},
      pages = {111--115},
      zblnumber = {},
      doi = {10.1007/978-94-017-3267-3_2},
      }
  • [GLN] Go to document R. Grigorchuk, D. Lenz, and T. Nagnibeda, "Schreier graphs of Grigorchuk’s group and a subshift associated to a nonprimitive substitution," in Groups, Graphs and Random Walks, Cambridge Univ. Press, Cambridge, 2017, vol. 436, pp. 250-299.
    @INCOLLECTION{GLN,
      author = {Grigorchuk, Rostislav and Lenz, Daniel and Nagnibeda, Tatiana},
      title = {Schreier graphs of {G}rigorchuk's group and a subshift associated to a nonprimitive substitution},
      booktitle = {Groups, Graphs and Random Walks},
      series = {London Math. Soc. Lecture Note Ser.},
      volume = {436},
      pages = {250--299},
      publisher = {Cambridge Univ. Press, Cambridge},
      year = {2017},
      mrclass = {37B50 (05C50 20D99)},
      mrnumber = {3644012},
      zblnumber = {1371.05123},
      doi = {10.1017/9781316576571},
      }
  • [grinek_en] Go to document R. I. Grigorchuk and V. V. Nekrashevich, "The group of asynchronous automata and rational homeomorphisms of the Cantor set," Mat. Zametki, vol. 67, iss. 5, pp. 680-685, 2000.
    @ARTICLE{grinek_en,
      author = {Grigorchuk, R. I. and Nekrashevich, V. V.},
      title = {The group of asynchronous automata and rational homeomorphisms of the {C}antor set},
      journal = {Mat. Zametki},
      fjournal = {Rossiĭskaya Akademiya Nauk. Matematicheskie Zametki},
      volume = {67},
      year = {2000},
      number = {5},
      pages = {680--685},
      issn = {0025-567X},
      mrclass = {37B15 (20F99 37B10 68Q45)},
      mrnumber = {1822615},
      doi = {10.1007/BF02676328},
      zblnumber = {0988.37014},
      }
  • [grineksu_en] Go to document R. I. Grigorchuk, V. V. Nekrashevich, and V. I. Sushchanskiui, "Automata, dynamical systems, and groups," Tr. Mat. Inst. Steklova, vol. 231, iss. Din. Sist., Avtom. i Beskon. Gruppy, pp. 134-214, 2000.
    @ARTICLE{grineksu_en,
      author = {Grigorchuk, R. I. and Nekrashevich, V. V. and Sushchanski\u\i, V. I.},
      title = {Automata, dynamical systems, and groups},
      journal = {Tr. Mat. Inst. Steklova},
      fjournal = {Trudy Matematicheskogo Instituta Imeni V. A. Steklova. Rossiĭskaya Akademiya Nauk},
      volume = {231},
      year = {2000},
      number = {Din. Sist., Avtom. i Beskon. Gruppy},
      pages = {134--214},
      issn = {0371-9685},
      mrclass = {37B15 (20F10 68Q45 68Q70)},
      mrnumber = {1841755},
      zblnumber = {1155.37311},
      url = {http://mi.mathnet.ru/eng/tm/v231/p134},
      }
  • [golod:nilalgebras] E. S. Golod, "On nil-algebras and finitely approximable $p$-groups," Izv. Akad. Nauk SSSR Ser. Mat., vol. 28, pp. 273-276, 1964.
    @ARTICLE{golod:nilalgebras,
      author = {Golod, E. S.},
      title = {On nil-algebras and finitely approximable {$p$}-groups},
      journal = {Izv. Akad. Nauk SSSR Ser. Mat.},
      fjournal = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
      volume = {28},
      year = {1964},
      pages = {273--276},
      issn = {0373-2436},
      mrclass = {16.32},
      mrnumber = {0161878},
      mrreviewer = {E. Inaba},
      zblnumber = {0215.39202},
     }
  • [gior:full] Go to document T. Giordano, I. F. Putnam, and C. F. Skau, "Full groups of Cantor minimal systems," Israel J. Math., vol. 111, pp. 285-320, 1999.
    @ARTICLE{gior:full,
      author = {Giordano, Thierry and Putnam, Ian F. and Skau, Christian F.},
      title = {Full groups of {C}antor minimal systems},
      journal = {Israel J. Math.},
      fjournal = {Israel Journal of Mathematics},
      volume = {111},
      year = {1999},
      pages = {285--320},
      issn = {0021-2172},
      mrclass = {46L55 (37B05 46L80 54H20)},
      mrnumber = {1710743},
      mrreviewer = {A. I. Danilenko},
      doi = {10.1007/BF02810689},
      zblnumber = {0942.46040},
      }
  • [greenleaf] F. P. Greenleaf, Invariant Means on Topological Groups, Van Nostrand Reinhold, New York, 1969.
    @BOOK{greenleaf,
      author = {Greenleaf, F. P.},
      title = {Invariant Means on Topological Groups},
      series = {Van Nostrand Mathematical Studies, No. 16},
      publisher = {Van Nostrand Reinhold, New York},
      year = {1969},
      zblnumber = {0174.19001},
      mrnumber = {0251549},
      }
  • [grigorchuk:80_en] R. I. Grigorchuk, "On Burnside’s problem on periodic groups," Funktsional. Anal. i Prilozhen., vol. 14, iss. 1, pp. 53-54, 1980.
    @ARTICLE{grigorchuk:80_en,
      author = {Grigorchuk, Rostislav I.},
      title = {On {B}urnside's problem on periodic groups},
      journal = {Funktsional. Anal. i Prilozhen.},
      fjournal = {Akademiya Nauk SSSR. Funktsional{\cprime}nyĭAnaliz i ego Prilozheniya},
      volume = {14},
      year = {1980},
      number = {1},
      pages = {53--54},
      issn = {0374-1990},
      mrclass = {20F05},
      mrnumber = {0565099},
      mrreviewer = {N. S. Chernikov},
      zblnumber = {0595.20029},
      }
  • [grigorchuk:milnor_en] Go to document R. I. Grigorchuk, "Milnor’s problem on the growth of groups," Sov. Math., Dokl., vol. 28, pp. 23-26, 1983.
    @ARTICLE{grigorchuk:milnor_en,
      author = {Grigorchuk, Rostislav I.},
      title = {Milnor's problem on the growth of groups},
      journal = {Sov. Math., Dokl.},
      volume = {28},
      year = {1983},
      pages = {23--26},
      zblnumber = {0547.20025},
      doi = {10.1515/9781400851317-027},
      }
  • [grigorchuk:growth_en] Go to document R. I. Grigorchuk, "Degrees of growth of finitely generated groups and the theory of invariant means," Math. USSR Izv., vol. 25, iss. 2, pp. 259-300, 1985.
    @ARTICLE{grigorchuk:growth_en,
      author = {Grigorchuk, Rostislav I.},
      title = {Degrees of growth of finitely generated groups and the theory of invariant means},
      journal = {Math. USSR Izv.},
      volume = {25},
      year = {1985},
      number = {2},
      pages = {259--300},
      zblnumber = {0583.20023},
      doi = {10.1070/IM1985v025n02ABEH001281},
      }
  • [grigorchuk:kyoto] R. I. Grigorchuk, "On growth in group theory," in Proceedings of the International Congress of Mathematicians, Vol. I, II, 1991, pp. 325-338.
    @INPROCEEDINGS{grigorchuk:kyoto,
      author = {Grigorchuk, Rostislav I.},
      title = {On growth in group theory},
      booktitle = {Proceedings of the {I}nternational {C}ongress of {M}athematicians, {V}ol. {I},
      {II}},
      venue = {{K}yoto, 1990},
      pages = {325--338},
      publisher = {Math. Soc. Japan, Tokyo},
      year = {1991},
      mrclass = {20-02 (20F32)},
      mrnumber = {1159221},
      mrreviewer = {Alexander Lubotzky},
      zblnumber = {0749.20016},
      }
  • [gri:solvedunsolved] Go to document R. Grigorchuk, "Solved and unsolved problems around one group," in Infinite Groups: Geometric, Combinatorial and Dynamical Aspects, Birkhäuser, Basel, 2005, vol. 248, pp. 117-218.
    @INCOLLECTION{gri:solvedunsolved,
      author = {Grigorchuk, Rostislav},
      title = {Solved and unsolved problems around one group},
      booktitle = {Infinite Groups: Geometric, Combinatorial and Dynamical Aspects},
      series = {Progr. Math.},
      volume = {248},
      pages = {117--218},
      publisher = {Birkhäuser, Basel},
      year = {2005},
      mrclass = {20-02 (20E08 20E18 20F10 20F38 20F50 20F65 20F69)},
      mrnumber = {2195454},
      mrreviewer = {Zoran {Š}unić},
      doi = {10.1007/3-7643-7447-0_5},
      zblnumber = {1165.20021},
      }
  • [gri:gap] Go to document R. Grigorchuk, "On the gap conjecture concerning group growth," Bull. Math. Sci., vol. 4, iss. 1, pp. 113-128, 2014.
    @ARTICLE{gri:gap,
      author = {Grigorchuk, Rostislav},
      title = {On the gap conjecture concerning group growth},
      journal = {Bull. Math. Sci.},
      fjournal = {Bulletin of Mathematical Sciences},
      volume = {4},
      year = {2014},
      number = {1},
      pages = {113--128},
      issn = {1664-3607},
      mrclass = {20F69 (20E07 20E08 20E18 20E26)},
      mrnumber = {3174281},
      mrreviewer = {Victor Petrogradsky},
      doi = {10.1007/s13373-012-0029-4},
      zblnumber = {1323.20035},
      }
  • [gro:gr] Go to document M. Gromov, "Groups of polynomial growth and expanding maps," Inst. Hautes Études Sci. Publ. Math., vol. 53, pp. 53-73, 1981.
    @ARTICLE{gro:gr,
      author = {Gromov, Mikhael},
      title = {Groups of polynomial growth and expanding maps},
      journal = {Inst. Hautes Études Sci. Publ. Math.},
      fjournal = {Institut des Hautes Études Scientifiques. Publications Mathématiques},
      volume = {53},
      year = {1981},
      pages = {53--73},
      issn = {0073-8301},
      mrclass = {53C20 (22E40 58F15)},
      mrnumber = {0623534},
      mrreviewer = {J. A. Wolf},
      url = {http://www.numdam.org/item?id=PMIHES_1981__53__53_0},
      zblnumber = {0474.20018},
      }
  • [gro:hyperb] Go to document M. Gromov, "Hyperbolic groups," in Essays in Group Theory, Springer, New York, 1987, vol. 8, pp. 75-263.
    @INCOLLECTION{gro:hyperb,
      author = {Gromov, M.},
      title = {Hyperbolic groups},
      booktitle = {Essays in Group Theory},
      series = {Math. Sci. Res. Inst. Publ.},
      volume = {8},
      pages = {75--263},
      publisher = {Springer, New York},
      year = {1987},
      mrclass = {20F32 (20F06 20F10 22E40 53C20 57R75 58F17)},
      mrnumber = {0919829},
      mrreviewer = {Christopher W. Stark},
      doi = {10.1007/978-1-4613-9586-7_3},
      zblnumber = {0634.20015},
      }
  • [gupta-sidkigroup] Go to document N. Gupta and S. Sidki, "On the Burnside problem for periodic groups," Math. Z., vol. 182, iss. 3, pp. 385-388, 1983.
    @ARTICLE{gupta-sidkigroup,
      author = {Gupta, Narain and Sidki, Saï},
      title = {On the {B}urnside problem for periodic groups},
      journal = {Math. Z.},
      fjournal = {Mathematische Zeitschrift},
      volume = {182},
      year = {1983},
      number = {3},
      pages = {385--388},
      issn = {0025-5874},
      mrclass = {20F50},
      mrnumber = {0696534},
      mrreviewer = {Seymour Bachmuth},
      doi = {10.1007/BF01179757},
      zblnumber = {0513.20024},
      }
  • [ivanov:burnside] Go to document S. V. Ivanov, "The free Burnside groups of sufficiently large exponents," Internat. J. Algebra Comput., vol. 4, iss. 1-2, p. ii, 1994.
    @ARTICLE{ivanov:burnside,
      author = {Ivanov, Sergei V.},
      title = {The free {B}urnside groups of sufficiently large exponents},
      journal = {Internat. J. Algebra Comput.},
      fjournal = {International Journal of Algebra and Computation},
      volume = {4},
      year = {1994},
      number = {1-2},
      pages = {ii+308},
      issn = {0218-1967},
      mrclass = {20F50 (20F05 20F06)},
      mrnumber = {1283947},
      mrreviewer = {A. Yu. Ol{\cprime}shanskii},
      doi = {10.1142/S0218196794000026},
      zblnumber = {0822.20044},
      }
  • [juschenkomonod] Go to document K. Juschenko and N. Monod, "Cantor systems, piecewise translations and simple amenable groups," Ann. of Math. (2), vol. 178, iss. 2, pp. 775-787, 2013.
    @ARTICLE{juschenkomonod,
      author = {Juschenko, Kate and Monod, Nicolas},
      title = {Cantor systems, piecewise translations and simple amenable groups},
      journal = {Ann. of Math. (2)},
      fjournal = {Annals of Mathematics. Second Series},
      volume = {178},
      year = {2013},
      number = {2},
      pages = {775--787},
      issn = {0003-486X},
      mrclass = {43A07 (20E32 54H20)},
      mrnumber = {3071509},
      mrreviewer = {Jorge Galindo},
      doi = {10.4007/annals.2013.178.2.7},
      zblnumber = {1283.37011},
      }
  • [JMMS:extensive] Go to document K. Juschenko, N. Matte Bon, N. Monod, and M. de la Salle, "Extensive amenability and an application to interval exchanges," Ergodic Theory Dynam. Systems, vol. 38, iss. 1, pp. 195-219, 2018.
    @article{JMMS:extensive,
      author = {Juschenko, Kate and {Matte~Bon},
      Nicolás and Monod, Nicolas and de~la Salle, Mikael},
      title = {Extensive amenability and an application to interval exchanges},
      journal = {Ergodic Theory Dynam. Systems},
      fjournal = {Ergodic Theory and Dynamical Systems},
      volume = {38},
      year = {2018},
      number = {1},
      pages = {195--219},
      mrnumber = {3742543},
      DOI = {10.1017/etds.2016.32},
      }
  • [YNS] Go to document K. Juschenko, V. Nekrashevych, and M. de la Salle, "Extensions of amenable groups by recurrent groupoids," Invent. Math., vol. 206, iss. 3, pp. 837-867, 2016.
    @ARTICLE{YNS,
      author = {Juschenko, Kate and Nekrashevych, Volodymyr and de la Salle, Mikael},
      title = {Extensions of amenable groups by recurrent groupoids},
      journal = {Invent. Math.},
      fjournal = {Inventiones Mathematicae},
      volume = {206},
      year = {2016},
      number = {3},
      pages = {837--867},
      issn = {0020-9910},
      mrclass = {22F50 (20E08 20F10 20F38 37B50 37C85 43A07 58H05)},
      mrnumber = {3573974},
      mrreviewer = {Laurent Bartholdi},
      doi = {10.1007/s00222-016-0664-6},
      zblnumber = {06664763},
      }
  • [kellendonLenz:aperiodicorder] J. Kellendonk, D. Lenz, and J. Savinien, Mathematics of Periodic Order, Birkhäuser/Springer, Basel, 2015, vol. 309.
    @BOOK{kellendonLenz:aperiodicorder,
      author = {Kellendonk, Johannes and Lenz, Daniel and Savinien, Jean},
      title = {Mathematics of Periodic Order},
      series = {Progr. Math. Phys.},
      volume = {309},
      publisher = {Birkhäuser/Springer, Basel},
      year = {2015},
      zblnumber = {1338.37005},
      }
  • [kassabovpak:oscillating] Go to document M. Kassabov and I. Pak, "Groups of oscillating intermediate growth," Ann. of Math. (2), vol. 177, iss. 3, pp. 1113-1145, 2013.
    @ARTICLE{kassabovpak:oscillating,
      author = {Kassabov, Martin and Pak, Igor},
      title = {Groups of oscillating intermediate growth},
      journal = {Ann. of Math. (2)},
      fjournal = {Annals of Mathematics. Second Series},
      volume = {177},
      year = {2013},
      number = {3},
      pages = {1113--1145},
      issn = {0003-486X},
      mrclass = {20F05 (20E08 20F69)},
      mrnumber = {3034295},
      mrreviewer = {Stephen P. Humphries},
      doi = {10.4007/annals.2013.177.3.7},
      zblnumber = {1283.20027},
      }
  • [krieger:homgroups] Go to document W. Krieger, "On a dimension for a class of homeomorphism groups," Math. Ann., vol. 252, iss. 2, pp. 87-95, 1979/80.
    @ARTICLE{krieger:homgroups,
      author = {Krieger, Wolfgang},
      title = {On a dimension for a class of homeomorphism groups},
      journal = {Math. Ann.},
      fjournal = {Mathematische Annalen},
      volume = {252},
      year = {1979/80},
      number = {2},
      pages = {87--95},
      issn = {0025-5831},
      mrclass = {46L35},
      mrnumber = {0593623},
      mrreviewer = {Horst Behncke},
      doi = {10.1007/BF01420115},
      zblnumber = {0472.54028},
      }
  • [kronecker:approximation] L. Kronecker, "N" aherunsgsweise ganzzahlige auflösung linearer gleichungen," in Monatsberichte Königlich Preussischen Akademie der Wissenschaften zu Berlin, , 1884, pp. 1179-1193, 1271.
    @INCOLLECTION{kronecker:approximation,
      author = {Kronecker, L.},
      title = {N\" aherunsgsweise ganzzahlige auflösung linearer gleichungen},
      booktitle = {Monatsberichte Königlich Preussischen Akademie der Wissenschaften zu Berlin},
      year = {1884},
      pages = {1179--1193, 1271--1299},
      zblnumber = {16.0083.02},
      }
  • [lysenok:burnside] Go to document I. G. Lysënok, "Infinite Burnside groups of even period," Izv. Ross. Akad. Nauk Ser. Mat., vol. 60, iss. 3, pp. 3-224, 1996.
    @ARTICLE{lysenok:burnside,
      author = {Lysënok, I. G.},
      title = {Infinite {B}urnside groups of even period},
      journal = {Izv. Ross. Akad. Nauk Ser. Mat.},
      fjournal = {Rossiĭskaya Akademiya Nauk. Izvestiya. Seriya Matematicheskaya},
      volume = {60},
      year = {1996},
      number = {3},
      pages = {3--224},
      issn = {1607-0046},
      mrclass = {20F50 (20F05 20F06)},
      mrnumber = {1405529},
      mrreviewer = {Victor S. Guba},
      doi = {10.1070/IM1996v060n03ABEH000077},
      zblnumber = {0926.20023},
      }
  • [mann:growth] Go to document A. Mann, How Groups Grow, Cambridge University Press, Cambridge, 2012, vol. 395.
    @BOOK{mann:growth,
      author = {Mann, Avinoam},
      title = {How Groups Grow},
      series = {London Math. Soc. Lect. Note Ser.},
      volume = {395},
      publisher = {Cambridge University Press, Cambridge},
      year = {2012},
      pages = {x+199},
      isbn = {978-1-107-65750-2},
      mrclass = {20F69 (20F05)},
      mrnumber = {2894945},
      mrreviewer = {Wolfgang Woess},
      zblnumber = {1253.20032},
      doi = {10.1017/CBO9781139095129},
      }
  • [matui:fullI] Go to document H. Matui, "Some remarks on topological full groups of Cantor minimal systems," Internat. J. Math., vol. 17, iss. 2, pp. 231-251, 2006.
    @ARTICLE{matui:fullI,
      author = {Matui, Hiroki},
      title = {Some remarks on topological full groups of {C}antor minimal systems},
      journal = {Internat. J. Math.},
      fjournal = {International Journal of Mathematics},
      volume = {17},
      year = {2006},
      number = {2},
      pages = {231--251},
      issn = {0129-167X},
      mrclass = {37B05 (37B10)},
      mrnumber = {2205435},
      mrreviewer = {Fred W. Roush},
      doi = {10.1142/S0129167X06003448},
      zblnumber = {1109.37008},
      }
  • [matui:etale] Go to document H. Matui, "Homology and topological full groups of étale groupoids on totally disconnected spaces," Proc. Lond. Math. Soc. (3), vol. 104, iss. 1, pp. 27-56, 2012.
    @ARTICLE{matui:etale,
      author = {Matui, Hiroki},
      title = {Homology and topological full groups of étale groupoids on totally disconnected spaces},
      journal = {Proc. Lond. Math. Soc. (3)},
      fjournal = {Proceedings of the London Mathematical Society. Third Series},
      volume = {104},
      year = {2012},
      number = {1},
      pages = {27--56},
      issn = {0024-6115},
      mrclass = {19D55 (22A22 46L55)},
      mrnumber = {2876963},
      mrreviewer = {Hiroyuki Osaka},
      doi = {10.1112/plms/pdr029},
      zblnumber = {1325.19001},
      }
  • [matui:expgrowth] Go to document H. Matui, "Some remarks on topological full groups of Cantor minimal systems II," Ergodic Theory Dynam. Systems, vol. 33, iss. 5, pp. 1542-1549, 2013.
    @ARTICLE{matui:expgrowth,
      author = {Matui, Hiroki},
      title = {Some remarks on topological full groups of {C}antor minimal systems {II}},
      journal = {Ergodic Theory Dynam. Systems},
      fjournal = {Ergodic Theory and Dynamical Systems},
      volume = {33},
      year = {2013},
      number = {5},
      pages = {1542--1549},
      issn = {0143-3857},
      mrclass = {37B10 (22A05 37B05 54H11)},
      mrnumber = {3103094},
      mrreviewer = {Fred W. Roush},
      doi = {10.1017/S0143385712000399},
      zblnumber = {1293.37010},
      }
  • [matui:fullonesided] Go to document H. Matui, "Topological full groups of one-sided shifts of finite type," J. Reine Angew. Math., vol. 705, pp. 35-84, 2015.
    @ARTICLE{matui:fullonesided,
      author = {Matui, Hiroki},
      title = {Topological full groups of one-sided shifts of finite type},
      journal = {J. Reine Angew. Math.},
      fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
      volume = {705},
      year = {2015},
      pages = {35--84},
      issn = {0075-4102},
      mrclass = {22A22 (37B10)},
      mrnumber = {3377390},
      mrreviewer = {Thomas Ward},
      doi = {10.1515/crelle-2013-0041},
      zblnumber = {1372.22006},
      }
  • [mattebon:liouville] Go to document N. Matte Bon, "Subshifts with slow complexity and simple groups with the Liouville property," Geom. Funct. Anal., vol. 24, iss. 5, pp. 1637-1659, 2014.
    @ARTICLE{mattebon:liouville,
      author = {Matte Bon, Nicolás},
      title = {Subshifts with slow complexity and simple groups with the {L}iouville property},
      journal = {Geom. Funct. Anal.},
      fjournal = {Geometric and Functional Analysis},
      volume = {24},
      year = {2014},
      number = {5},
      pages = {1637--1659},
      issn = {1016-443X},
      mrclass = {37B50 (20F65 60B15)},
      mrnumber = {3261637},
      mrreviewer = {Samy Abbes},
      doi = {10.1007/s00039-014-0293-4},
      zblnumber = {1366.37040},
      }
  • [mattebon:grigochuk] Go to document N. Matte Bon, "Topological full groups of minimal subshifts with subgroups of intermediate growth," J. Mod. Dyn., vol. 9, pp. 67-80, 2015.
    @ARTICLE{mattebon:grigochuk,
      author = {Matte Bon, Nicolás},
      title = {Topological full groups of minimal subshifts with subgroups of intermediate growth},
      journal = {J. Mod. Dyn.},
      fjournal = {Journal of Modern Dynamics},
      volume = {9},
      year = {2015},
      pages = {67--80},
      issn = {1930-5311},
      mrclass = {37B10 (20F99)},
      mrnumber = {3395261},
      mrreviewer = {Alfredo M. G. Costa},
      doi = {10.3934/jmd.2015.9.67},
      zblnumber = {1352.37037},
      }
  • [milnor:5603] J. Milnor, "Problem 5603," Amer. Math. Monthly, vol. 75, pp. 685-686, 1968.
    @ARTICLE{milnor:5603,
      author = {Milnor, John},
      title = {Problem 5603},
      journal = {Amer. Math. Monthly},
      volume = {75},
      year = {1968},
      pages = {685--686},
      zblnumber = {},
      }
  • [kourovka] V. D. Mazurov and E. ~I. Khukhro, Unsolved problems in group theory. The Kourovka notebook. no. 18, 2014.
    @MISC{kourovka,
      author = {Mazurov, V. D. and Khukhro, E.~I.},
      title = {Unsolved problems in group theory. {T}he {K}ourovka notebook. no. 18},
      arxiv = {1401.0300},
      year = {2014},
      zblnumber = {},
      }
  • [novikovadjan] Go to document P. S. Novikov and S. I. Adian, "Infinite periodic groups. I," Izv. Akad. Nauk SSSR Ser. Mat., vol. 32, pp. 212-244, 1968.
    @ARTICLE{novikovadjan,
      author = {Novikov, P. S. and Adian, S. I.},
      title = {Infinite periodic groups. {I}},
      journal = {Izv. Akad. Nauk SSSR Ser. Mat.},
      fjournal = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
      volume = {32},
      year = {1968},
      pages = {212--244},
      issn = {0373-2436},
      mrclass = {20.15},
      mrnumber = {0240178},
      zblnumber = {0194.03301},
      doi = {10.1070/IM1968v002n01ABEH000637},
      }
  • [nek:book] Go to document V. Nekrashevych, Self-Similar Groups, American Mathematical Society, Providence, RI, 2005, vol. 117.
    @BOOK{nek:book,
      author = {Nekrashevych, Volodymyr},
      title = {Self-Similar Groups},
      series = {Math. Surveys Monogr.},
      volume = {117},
      publisher = {American Mathematical Society, Providence, RI},
      year = {2005},
      pages = {xii+231},
      isbn = {0-8218-3831-8},
      mrclass = {20E08 (20F65 37B15 37F10)},
      mrnumber = {2162164},
      mrreviewer = {Laurent Bartholdi},
      doi = {10.1090/surv/117},
      zblnumber = {1087.20032},
      }
  • [nek:fullgr] Go to document V. Nekrashevych, "Simple groups of dynamical origin," Ergodic Theory Dynam. Systems, p. 26, 2015.
    @article{nek:fullgr,
      author = {Nekrashevych, Volodymyr},
      title = {Simple groups of dynamical origin},
      journal = {Ergodic Theory Dynam. Systems},
      fjournal = {Ergodic Theory and Dynamical Systems},
      note = {published online: 17 August 2017},
      pages = {26 pp.},
      year = {2015},
      doi = {10.1017/etds.2017.47},
      }
  • [olshanskii:nonamenable] Go to document Y. A. Olcprimeshanskii, "On the question of the existence of an invariant mean on a group," Uspekhi Mat. Nauk, vol. 35, iss. 4(214), pp. 199-200, 1980.
    @ARTICLE{olshanskii:nonamenable,
      author = {Ol{\cprime}shanskii, A. Yu},
      title = {On the question of the existence of an invariant mean on a group},
      journal = {Uspekhi Mat. Nauk},
      fjournal = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk},
      volume = {35},
      year = {1980},
      number = {4(214)},
      pages = {199--200},
      issn = {0042-1316},
      mrclass = {43A07},
      mrnumber = {0586204},
      mrreviewer = {M. Bo\.zejko},
      zblnumber = {0452.20032},
      doi = {10.1070/RM1980v035n04ABEH001876},
      }
  • [olshanski:monster] Y. A. Olcprimeshanskii, "Groups of bounded period with subgroups of prime order," Algebra i Logika, vol. 21, iss. 5, pp. 553-618, 1982.
    @ARTICLE{olshanski:monster,
      author = {Ol{\cprime}shanskii, A. Yu.},
      title = {Groups of bounded period with subgroups of prime order},
      journal = {Algebra i Logika},
      fjournal = {Akademiya Nauk SSSR. Sibirskoe Otdelenie. Institut Matematiki. Algebra i Logika},
      volume = {21},
      year = {1982},
      number = {5},
      pages = {553--618},
      issn = {0373-9252},
      mrclass = {20F50 (20E15)},
      mrnumber = {0721048},
      mrreviewer = {Yu. I. Merzlyakov},
      zblnumber = {},
      }
  • [olshanski:book] Go to document Y. A. Olcprimeshanskii, Geometry of Defining Relations in Groups, Kluwer Academic Publishers Group, Dordrecht, 1991, vol. 70.
    @BOOK{olshanski:book,
      author = {Ol{\cprime}shanskii, A. Yu.},
      title = {Geometry of Defining Relations in Groups},
      series = {Math. Appl. (Soviet Series)},
      volume = {70},
      note = {translated from the 1989 Russian original by Yu. A. Bakhturin},
      publisher = {Kluwer Academic Publishers Group, Dordrecht},
      year = {1991},
      pages = {xxvi+505},
      isbn = {0-7923-1394-1},
      mrclass = {20F32 (20E10 57M07)},
      mrnumber = {1191619},
      doi = {10.1007/978-94-011-3618-1},
      zblnumber = {0732.20019},
     }
  • [olshanski:residualing] Go to document Y. A. Olcprimeshanskii, "On residualing homomorphisms and $G$-subgroups of hyperbolic groups," Internat. J. Algebra Comput., vol. 3, iss. 4, pp. 365-409, 1993.
    @ARTICLE{olshanski:residualing,
      author = {Ol{\cprime}shanskii, A. Yu.},
      title = {On residualing homomorphisms and {$G$}-subgroups of hyperbolic groups},
      journal = {Internat. J. Algebra Comput.},
      fjournal = {International Journal of Algebra and Computation},
      volume = {3},
      year = {1993},
      number = {4},
      pages = {365--409},
      issn = {0218-1967},
      mrclass = {20F32 (20F05 20F06 57M07)},
      mrnumber = {1250244},
      mrreviewer = {Michel Coornaert},
      doi = {10.1142/S0218196793000251},
      zblnumber = {0830.20053},
      }
  • [paterson:amenability] Go to document A. L. T. Paterson, Amenability, American Mathematical Society, Providence, RI, 1988, vol. 29.
    @BOOK{paterson:amenability,
      author = {Paterson, Alan L. T.},
      title = {Amenability},
      series = {Math. Surveys Monogr.},
      volume = {29},
      publisher = {American Mathematical Society, Providence, RI},
      year = {1988},
      pages = {xx+452},
      isbn = {0-8218-1529-6},
      mrclass = {43-02 (22-02 43A07 46Lxx)},
      mrnumber = {0961261},
      mrreviewer = {C. Chou},
      doi = {10.1090/surv/029},
      zblnumber = {0648.43001},
      }
  • [rips:cancellation] Go to document E. Rips, "Generalized small cancellation theory and applications. I. The word problem," Israel J. Math., vol. 41, iss. 1-2, pp. 1-146, 1982.
    @ARTICLE{rips:cancellation,
      author = {Rips, E.},
      title = {Generalized small cancellation theory and applications. {I}. {T}he word problem},
      journal = {Israel J. Math.},
      fjournal = {Israel Journal of Mathematics},
      volume = {41},
      year = {1982},
      number = {1-2},
      pages = {1--146},
      issn = {0021-2172},
      mrclass = {20F06},
      mrnumber = {0657850},
      mrreviewer = {D. E. Cohen},
      doi = {10.1007/BF02760660},
      zblnumber = {0508.20017},
      }
  • [sunic:hausdorff] Go to document Z. vSunić, "Hausdorff dimension in a family of self-similar groups," Geom. Dedicata, vol. 124, pp. 213-236, 2007.
    @ARTICLE{sunic:hausdorff,
      author = {{Š}unić, Zoran},
      title = {Hausdorff dimension in a family of self-similar groups},
      journal = {Geom. Dedicata},
      fjournal = {Geometriae Dedicata},
      volume = {124},
      year = {2007},
      pages = {213--236},
      issn = {0046-5755},
      mrclass = {20E08 (20E18 20F50 20F69)},
      mrnumber = {2318546},
      mrreviewer = {Laurent Bartholdi},
      doi = {10.1007/s10711-006-9106-8},
      zblnumber = {1169.20015},
      }
  • [sushch:periodic] V. Ī. Suvsvcanscprimekiui, "Periodic $p$-groups of permutations and the unrestricted Burnside problem," Dokl. Akad. Nauk SSSR, vol. 247, iss. 3, pp. 557-561, 1979.
    @ARTICLE{sushch:periodic,
      author = {Su{š}\v{c}ans{\cprime}kiĭ,
      V. Ī.},
      title = {Periodic {$p$}-groups of permutations and the unrestricted {B}urnside problem},
      journal = {Dokl. Akad. Nauk SSSR},
      fjournal = {Doklady Akademii Nauk SSSR},
      volume = {247},
      year = {1979},
      number = {3},
      pages = {557--561},
      issn = {0002-3264},
      mrclass = {20B35},
      mrnumber = {0545692},
      mrreviewer = {L. A. Kurdachenko},
      zblnumber = {0428.20023},
      }
  • [vneumann:masses] J. von Neumann, "Zur allgemeinen Theorie des Masses," in Collected Works, Vol., , 1929, vol. 13, pp. 73-116, 333, 599.
    @INCOLLECTION{vneumann:masses,
      author = {von Neumann, John},
      title = {Zur allgemeinen {Theorie} des {Masses}},
      series = {Fund. Math.},
      volume = {13},
      year = {1929},
      pages = {73--116, 333, 599--643},
      booktitle = {Collected Works, Vol.},
      zblnumber = {55.0151.01},
      }
  • [vorob:schreiergraphs] Go to document Y. Vorobets, "Notes on the Schreier graphs of the Grigorchuk group," in Dynamical Systems and Group Actions, Amer. Math. Soc., Providence, RI, 2012, vol. 567, pp. 221-248.
    @INCOLLECTION{vorob:schreiergraphs,
      author = {Vorobets, Yaroslav},
      title = {Notes on the {S}chreier graphs of the {G}rigorchuk group},
      booktitle = {Dynamical Systems and Group Actions},
      series = {Contemp. Math.},
      volume = {567},
      pages = {221--248},
      publisher = {Amer. Math. Soc., Providence, RI},
      year = {2012},
      mrclass = {37A15 (05C90 22F05 37B05)},
      mrnumber = {2931920},
      mrreviewer = {Alain Valette},
      doi = {10.1090/conm/567/11250},
      zblnumber = {1255.05192},
      }
  • [wagon:banachtarski] S. Wagon, The Banach-Tarski Paradox, Cambridge University Press, Cambridge, 1993.
    @BOOK{wagon:banachtarski,
      author = {Wagon, Stan},
      title = {The {B}anach-{T}arski Paradox},
      note = {with a foreword by Jan Mycielski, corrected reprint of the 1985 original},
      publisher = {Cambridge University Press, Cambridge},
      year = {1993},
      pages = {xviii+253},
      isbn = {0-521-45704-1},
      mrclass = {04A25 (03E25 04-02 04A15 28-02 43A05)},
      mrnumber = {1251963},
      zblnumber = {1372.43001},
      }
  • [wilf:algorithms] Go to document H. S. Wilf, Combinatorial Algorithms: An Update, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989, vol. 55.
    @BOOK{wilf:algorithms,
      author = {Wilf, Herbert S.},
      title = {Combinatorial Algorithms: An Update},
      series = {CBMS-NSF Reg. Conf. Ser. Appl. Math.},
      volume = {55},
      publisher = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA},
      year = {1989},
      pages = {vi+47},
      isbn = {0-89871-231-9},
      mrclass = {05-02 (05-04 05A05 68-02 68R05)},
      mrnumber = {0993775},
      mrreviewer = {Peter Eades},
      doi = {10.1137/1.9781611970166},
      zblnumber = {0695.05002},
      }
  • [zelmanov:burnside] Go to document E. I. Zelcprimemanov, "Solution of the restricted Burnside problem for groups of odd exponent," Izv. Akad. Nauk SSSR Ser. Mat., vol. 54, iss. 1, pp. 42-59, 221, 1990.
    @ARTICLE{zelmanov:burnside,
      author = {Zel{\cprime}manov, E. I.},
      title = {Solution of the restricted {B}urnside problem for groups of odd exponent},
      journal = {Izv. Akad. Nauk SSSR Ser. Mat.},
      fjournal = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
      volume = {54},
      year = {1990},
      number = {1},
      pages = {42--59, 221},
      issn = {0373-2436},
      mrclass = {20F50 (20D10 20F40)},
      mrnumber = {1044047},
      mrreviewer = {J. Wiegold},
      zblnumber = {0752.20017},
      doi = {10.1070/IM1991v036n01ABEH001946},
     }

Authors

Volodymyr Nekrashevych

Texas A&M University, College Station, TX