A Note About Configuration of A Group

Abstract

In 2001, Rosenblatt and Willis defined the concept of configuration of a group to give a condition for amenability of groups. In this paper, we study the relation between configuration and commutator subgroup G' of G and prove that if G(1) and G(2) are two finitely generated groups with the same configuration set, then cl c2 and if G'1 and G(2) are finite, then G'(1) G. Also, we prove that if two free finitely generated Burnside groups of finite exponent have the same configuration set, then they must be isomorphic.