International Journal of Group Theory (Sep 2015)
On central endomorphisms of a group
Abstract
Let Γ be a normal subgroup of the full automorphism group Aut(G) of a group G , and assume that Inn(G)≤Γ . An endomorphism σ of G is said to be {\it Γ -central} if σ induces the the identity on the factor group G/C G (Γ) . Clearly, if Γ=Inn(G) , then a Γ -central endomorphism is a {\it central} endomorphism. In this article the conditions under which a Γ -central endomorphism of a group is an automorphism are investigated.
