Illinois Journal of Mathematics

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 $G_2$ are two finitely generated groups having the same configuration sets and $G_1$ satisfies a semigroup law, then $G_2$ satisfies the same semigroup law. Furthermore, if $G_1$ is abelian then $G_1$ and $G_2$ are isomorphic.

Article information

Source
Illinois J. Math. Volume 48, Number 3 (2004), 861-873.

Dates
First available: 13 November 2009

http://projecteuclid.org/euclid.ijm/1258131056

Mathematical Reviews number (MathSciNet)
MR2114255

Zentralblatt MATH identifier
1067.43001

Subjects
Primary: 43A07: Means on groups, semigroups, etc.; amenable groups
Secondary: 20F99: None of the above, but in this section

Citation

Abdollahi, Alireza; Rejali, Ali; Willis, George A. Group properties characterised by configurations. Illinois Journal of Mathematics 48 (2004), no. 3, 861--873. http://projecteuclid.org/euclid.ijm/1258131056.