Solubility of groups can be characterized by configuration

Abstract

The concept of configuration was first introduced by Rosenblatt and Willis to give a characterization for the amenability of groups. We show that group properties of being soluble or FC can be characterized by configuration sets. Then we investigate some condition on configuration pairs, which leads to isomorphism. We introduce a somewhat different notion of configuration equivalence, namely strong configuration equivalence, and prove that strong configuration equivalence coincides with isomorphism.