On autocentral kernel of groups

Document Type : Research Paper

Authors

Department of Mathematics, University of Birjand, Birjand, Iran

Abstract

‎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.

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References

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History

  • Receive Date: 02 January 2025
  • Revise Date: 06 May 2025
  • Accept Date: 18 May 2025

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