On M-autocenter and M-autocommutator of group G

‎Let $G$ be a group and $\text{Aut}(G)$ be the full automorphisms group of $G$‎. ‎The absolute center $L(G)$ of a group $G$ is the subgroup of all elements fixed by every automorphism of $G$‎. ‎We know that if $G/L(G)$ is finite then so is $\text{Aut}(G)$‎. ‎In this paper we introduce a new concept of certain subgroup of $G$‎, ‎which is in a way a generalized version of autocenter and prove some results in this regard‎