Wachstum von endlich erzeugten Gruppen
(Growth of finitely generated groups, transl.)

by Claas Röver

Abstract

The first part of this work is mainly a collection of old results about the connection between the algebraic structure of a finitely generated group and its growth. I mostly consider residually finite groups and theorems of the following type: If G is a group with the group theoretic property P then G has either exponential or polynomial growth.

Then I give a full proof of the fact due to Grigorchuk that there are groups of intermediate growth. For residually finite-p groups the relationship with Lie algebras is also described.

In the final chapter I proof that every finitely generated group G with finite abelianization can be embedded in a 2-generated group G* of the same growth type, i.e. both have polynomial growth, intermediate growth, or exponential growth. Moreover, G* can be chosen to be residually finite (P-periodic or conjugacy seperable) whenever G is residually finite (P-periodic or conjugacy seperable); here P is a set of primes.

The full work (in german) is downloadable as gzipped dvi (68 kB), post-script (254 kB), or pdf (170 kB) files.