Illinois Journal of Mathematics

Group properties characterised by configurations

Alireza Abdollahi,Ali Rejali, and George A. Willis

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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

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

First available: 13 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Abdollahi, Alireza; Rejali, Ali; Willis, George A. Group properties characterised by configurations. Illinois Journal of Mathematics 48 (2004), no. 3, 861--873.

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