Groups of oscillating intermediate growth


We construct an uncountable family of finitely generated groups of intermediate growth, with growth functions of new type. These functions can have large oscillations between lower and upper bounds, both of which come from a wide class of functions. In particular, we can have growth oscillating between $e^{n^\alpha}$ and any prescribed function, growing as rapidly as desired. Our construction is built on top of any of the Grigorchuk groups of intermediate growth and is a variation on the limit of permutational wreath product.


Martin Kassabov

Mathematics, University of Southampton, Southampton SO17 1BG
United Kingdom, and
Department of Mathematics
Cornell University
Ithaca, NY 14853-4201

Igor Pak

Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, CA 90095-1555