Square commutative groups

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 $\hat{G}$ is an abelian group, then we give conditions for a group generated by two elements, with additional conditions, to be a square commutative group.

10 pages, added Corollary 2.8, Corollary 3.5 and Theorem 4.8