Group properties characterised by configurations

Abstract

J. M. Rosenblatt and G. A. Willis introduced the notion of configurations for finitely generated groups G. They characterised amenability of G in terms of the configuration equations. In this paper we investigate which group properties can be characterised by configurations. It is proved that if G 1 and G2 are two finitely generated groups having the same configuration sets and G1 satisfies a semigroup law, then G 2 satisfies the same semigroup law. Furthermore, if G1 is abelian then G1 and G2 are isomorphic. ©2004 University of Illinois.