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^{-۱}\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.

کلیدواژه ها:

Absolute central automorphisms‎ ، ‎Absolute centre‎ ، ‎Autocentral kernel‎ ، ‎Autonilpotent group