Abstract
This paper deals with finite groups. J. L. Brenner and James Wiegold defined a finite group G as lying in Γ1(2) if G is nonabelian and for every 1≠x ∈ G, either x is an involution and G = ⟨x,y⟩ for some y ∈ G or x is not an involution and there is an involution z ∈ G with G = ⟨x,z⟩. In this paper we expand the work of J. L. Brenner and James Wiegold, and that of Martin J. Evans in the investigation of which finite groups lie in Γ1(2).