Research ArticleNo Access

A note on Hall normally embedded subgroups of finite groups

Xuanli He

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

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Qinhui Sun

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

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Qinghong Guo

School of Mathematics and Statistics, Central South University, New Campus, Changsha, Hunan 410083, P. R. China

Department of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P. R. China

E-mail Address: qhguo1009@163.com

Corresponding author.

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https://doi.org/10.1142/S0219498825501397Cited by:1 (Source: Crossref)

Abstract

Let $G$ $G$ be a finite group. A subgroup $H$ $H$ of $G$ $G$ is called Hall normally embedded in $G$ $G$ if $H$ $H$ is a Hall subgroup of the normal closure $H^{G}$ $H^{G}$ . In this paper, we fix a subgroup $D$ $D$ of Sylow subgroup $P$ $P$ of $G$ $G$ with $1 < | D | < | P |$ $1 < | D | < | P |$ and study the structure of $G$ $G$ under the assumption that all subgroups $H$ $H$ of $P$ $P$ with $| H | = | D |$ $| H | = | D |$ are Hall normally embedded in $G$ $G$ .

Communicated by Mark L. Lewis

Keywords:

AMSC: 20D10, 20D20

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