- Group properties characterised by configurations
- Abdollahi, Alireza; Rejali, Ali; Willis, George A.
- Illinois Journal of Mathematics Vol. 48, Issue 3, p. 861-873
- University Of Illinois, Department of Mathematics
- Resource Type
- journal article
- 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 G₁ and G₂ are two finitely generated groups having the same configuration sets and G₁ satisfies a semigroup law, then G₂ satisfies the same semigroup law. Furthermore, if G₁ is abelian then G₁ and G₂ are isomorphic.
- finitely generated groups; configuration equations; isomorphism; abelian groups
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