Two-sided configuration equivalence and isomorphism

TL;DR

This paper explores conditions under which two-sided configuration equivalence implies isomorphism in certain classes of groups, extending understanding of group structure characterization.

Contribution

It introduces a new class of groups, including polycyclic and FC groups, where two-sided configuration equivalence and isomorphism are equivalent.

Findings

Two-sided configuration equivalence coincides with isomorphism in the new group class.

The class includes polycyclic and FC groups.

Provides a framework for characterizing group structures via configurations.

Abstract

The concept of configuration was first introduced to give a characterization for the amenability of groups. Then the concept of two-sided configuration was suggested to provide normality to study the group structures more efficiently. It has been interesting that for which groups, two-sided configuration equivalence would imply isomorphism. We introduce a class of groups, containing polycyclic and FC groups, which for them, the notions of two-sided configuration equivalence and isomorphism coincide.