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 G1 and G2 are two finitely generated groups with the same configuration set, then G1/G'1 = G2/G'2 and if G'1 and G'2 are finite, then G'1 = G'2 2. Also, we prove that if two free finitely generated Burnside groups of finite exponent have the same configuration set, then they must be isomorphic. Keywords: Configuration; Amenability; Commutator Subgroup, Burnside Group 2010 Mathematics Subject Classification: 20F24, 43A07.