Finite groups with some $\mathcal{HC}-$subgroups

Articles in Press

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.

Abstract

Let $G$ be a finite group. A subgroup $H$ of $G$ is called an $\mathcal{H}{-}$subgroup in $G$ if $H^{g}\cap N_{G}(H)\leq H$ for all $g\in G.$ A subgroup $H$ of $G$ is called an $\mathcal{H}{ C-}$subgroup in $G$ if there exists a normal subgroup $T$ of $G$ such that $G=HT$ and $H^{g}\cap N_{T}(H)\leq H$ for all $g\in G.$ In this paper, we give some new criteria for $p-$nilpotency and supersolvability of a group $G$ when certain subgroups of prime power orders of $G$ are $\mathcal{H}{ C-}$subgroups.

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References

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Algebraic Structures and Their Applications

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Available Online from 27 January 2026

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