Some Remarks on Conjugate Closed Groups

Abstract

Conjugate closed groups, which are briefly called CC − Groups, form a proper subclass of T − Groups. We prove that if G = Z(G) × H, then G is conjugate closed if and only if H is conjugate closed. We also show that a finite group G is semisimple, conjugate closed and perfect if and only if it is a direct product of non-abelian and simple groups.