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On weakly $ℋ C$ -embedded subgroups of finite groups

M. Asaad

Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

E-mail Address: moasmo45@hotmail.com

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and

M. Ramadan

Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

E-mail Address: mramadan12@yahoo.com

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https://doi.org/10.1142/S0219498816500778Cited by:8 (Source: Crossref)

Abstract

Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be an $ℋ C$ -subgroup of $G$ if there exists a normal subgroup $T$ of $G$ such that $G = H T$ and $H^{g} \cap N_{T} (H) \leq H$ for all $g \in G .$ We say that $H$ is weakly $ℋ C$ -embedded in $G$ if there exists a normal subgroup $T$ of $G$ such that $H^{G} = H T$ and $H^{g} \cap N_{T} (H) \leq H$ for all $g \in G$ . In this paper, we investigate the structure of the finite group $G$ under the assumption that some subgroups of prime power order are weakly $ℋ C$ -embedded in $G$ . Our results improve and generalize several recent results in the literature.

Communicated by D. Passman

Keywords:

AMSC: 20D10, 20D15, 20D20

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