Configuration of nilpotent groups and isomorphism

Abstract

The concept of configuration was first introduced by Rosenblatt and Willis to give a condition for amenability of groups. We show that if G1 and G2 have the same configuration sets and H1 is a normal subgroup of G1 with abelian quotient, then there is a normal subgroup H2 of G2 such that G1/H1 ≅ G2/H2. Also configuration of FC-groups and isomorphism is studied. © World Scientific Publishing Company.