ON autocentral kernel of a group

Abstract

‎Let $G$ be a group‎, ‎$Aut(G)$ and $L(G)$ denote the full automorphisms group and absolute center of $G$‎, ‎respectively‎. ‎An automorphism $\alpha \in Aut(G)$ is called autocentral automorphism if $g^{-1}\alpha(g) \in L(G)$‎, ‎for all $g \in G $‎. ‎In this talk‎, ‎the elements of a group that are fixed by any autocentral automorphism are identified‎. ‎Moreover‎, ‎the autocentral kernel of $G$ is introduced and some properties of autocentral automorphisms of $G$ are also given‎.