On central endomorphisms of a group

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

کلیدواژه ها:

central endomorphism ، autocentral endomorphism ، purely non-abelian group