Open Access
Translator Disclaimer
Fall 2004 Group properties characterised by configurations
Alireza Abdollahi, Ali Rejali, George A. Willis
Illinois J. Math. 48(3): 861-873 (Fall 2004). DOI: 10.1215/ijm/1258131056

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.

Citation

Download Citation

Alireza Abdollahi. Ali Rejali. George A. Willis. "Group properties characterised by configurations." Illinois J. Math. 48 (3) 861 - 873, Fall 2004. https://doi.org/10.1215/ijm/1258131056

Information

Published: Fall 2004
First available in Project Euclid: 13 November 2009

zbMATH: 1067.43001
MathSciNet: MR2114255
Digital Object Identifier: 10.1215/ijm/1258131056

Subjects:
Primary: ‎43A07‎
Secondary: 20F99

Rights: Copyright © 2004 University of Illinois at Urbana-Champaign

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.48 • No. 3 • Fall 2004
Back to Top