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Finite groups with $n$ -embedded subgroups

Qinghong Guo

College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, P. R. China

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Xuanli He

College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, P. R. China

E-mail Address: hxlczh@gxu.edu.cn

Corresponding author.

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Muhong Huang

College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, P. R. China

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https://doi.org/10.1142/S0218196721500508Cited by:2 (Source: Crossref)

Abstract

Let $G$ be a finite group. How minimal subgroups can be embedded in $G$ is a question of particular interest in studying the structure of $G$ . A subgroup $H$ of $G$ is called $s$ -permutable in $G$ if $H P = P H$ for all Sylow subgroups $P$ of $G$ . A subgroup $H$ of $G$ is called $n$ -embedded in $G$ if there exists a normal subgroup $T$ of $G$ such that $H^{G} = H T$ and $H \cap T \leq H_{s G}$ , where $H_{s G}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are $s$ -permutable in $G$ . In this paper, we investigate the structure of the finite group $G$ with $n$ -embedded subgroups.

Communicated by O. Kharlampovich

Keywords:

AMSC: 20D10, 20D20

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