A finitary version of Gromov's polynomial growth theorem

Details A finitary version of Gromov's polynomial growth theorem A finitary version of Gromov's polynomial growth theorem

2009-10-21

arxiv.org/abs/0910.4148v2

Mathematics

Group Theory

43 pages, no figures, to appear, GAFA. This is the final version; referee corrections have been incorporated, and some additio

Scientific paper

We show that for some absolute (explicit) constant $C$, the following holds for every finitely generated group $G$, and all $d >0$: If there is some $ R_0 > \exp(\exp(Cd^C))$ for which the number of elements in a ball of radius $R_0$ in a Cayley graph of $G$ is bounded by $R_0^d$, then $G$ has a finite index subgroup which is nilpotent (of step $

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