on autocentral kernel of groups

Let $g$ be a group, where $text{aut}(g)$ denotes the full automorphisms group of $g$ and $l(g)$ represents the absolute center of $g.$ an automorphism $alpha in text{aut}(g)$ is called an autocentral automorphism if $g^{-1}alpha(g) in l(g),$ for all $g in g .$ in this paper, we introduce the notion of autocentral kernel subgroup for an arbitrary group $g.$ we then investigate and establish several structural properties of this subgroup, providing insights into its role within the broader framework of group theory.