Abstract
We provide the first examples of finitely generated simple groups that are amenable (and infinite). To this end, we prove that topological full groups of minimal systems are amenable. This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suitable family of densities on the classical Bernoulli space.
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[Bezuglyi-Medynets]
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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},
CODEN = {CQMAAQ},
MRCLASS = {37B05 (20B99 28A60 28D05 37A20)},
MRNUMBER = {2353913},
MRREVIEWER = {Jan Kwiatkowski},
DOI = {10.4064/cm110-2-6},
ZBLNUMBER = {1142.37011},
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NOTE={to appear in \emph{Proc. Amer. Math. Soc.}},
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}
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