On central endomorphisms of a group

Abstract

Let be a normal subgroup of the full automorphism group Aut(G) of a group G, and assume that Inn(G) . An endomorphism of G is said to be -central if induces the the identity on the factor group G=CG(). Clearly, if = Inn(G), then a -central endomorphism is a central endomorphism. In this article the conditions under which a -central endomorphism of a group is an automorphism are investigated.