Some properties of autocentral automorphisms of a group

摘要

Let G be a group, Aut(G) and L(G) denote the full automorphisms group and absolute centre of G, respectively. The automorphism ${alphain Aut(G)}$ is called autocentral if ${g^{-1}alpha(g)in L(G)}$ , for all ${gin G}$ . In the present paper, we investigate the properties of such automorphisms.