Research ArticleNo Access

On weakly $ℋ$ -subgroups of finite groups III

Ruifang Chen

College of Mathematics and Information Science, Henan Normal University 453007, Henan, P. R. China

E-mail Address: fang119128@126.com

Corresponding author.

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and

Xianhe Zhao

College of Mathematics and Information Science, Henan Normal University 453007, Henan, P. R. China

E-mail Address: zhaoxianhe989@163.com

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https://doi.org/10.1142/S0219498824500622Cited by:0 (Source: Crossref)

Abstract

Let $G$ be a group. A subgroup $H$ of $G$ is called an $ℋ$ -subgroup in $G$ if $N_{G} (H) \cap H^{x} \leq H$ for all $x \in G$ . Furthermore, a subgroup $H$ of $G$ is called a weakly $ℋ$ -subgroup in $G$ if there exists a normal subgroup $K$ of $G$ such that $G = H K$ and $H \cap K$ is an $ℋ$ -subgroup in $G$ . In this paper, some new criteria for a group to be $p$ -nilpotent and supersolvable are given.

Communicated by M. L. Lewis

Keywords:

AMSC: 20D10, 20D20

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