Strong Configuration Equivalence and Isomorphism

Ali Rejali, Meisam Soleimani Malekan

Published 2015-10-25Version 1

The concept of configuration was first introduced by Rosenblatt and Willis to give a condition for amenability of groups. We show that if $G$ and $H$ are two configuration equivalent groups, then they satisfy in same group laws. Also, solubility, being FC are properties can be translated by configuration. At end, we introduce a somewhat different notion of configuration equivalence, namely strongly configuration equivalence, and prove this new definition leads to isomorphism.