Square commutative groups

TL;DR

This paper characterizes square commutative groups by linking their structure to the abelian property of their dual groups, providing specific conditions for groups generated by two elements.

Contribution

It establishes a necessary and sufficient condition for groups to be square commutative based on their dual groups and explores conditions for two-generated groups.

Findings

A group is square commutative if and only if its dual is abelian.

Provides criteria for two-generated groups to be square commutative.

Characterizes the structure of square commutative groups in terms of generators.

Abstract

In this paper we first give a necessary and sufficient condition for a group $G$ generated by $n$ elements to be a square commutative group and prove $G$ is a square commutative group if and only if $\widehat{G}$ is an abelian group, then we give conditions for a group generated by two elements, with additional conditions, to be a square commutative group.