Research ArticleNo Access

Finite groups with some minimal subgroups are $ℋ C$ -subgroups

Xianbiao Wei

School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230022, P. R. China

https://doi.org/10.1142/S0219498817500621Cited by:0 (Source: Crossref)

Abstract

A subgroup $H$ of a group $G$ is said to be an $ℋ C$ -subgroup of $G$ , if there exists a normal subgroup $K$ of $G$ such that $G = H K$ and $H^{g} \cap N_{K} (H) \leq H$ , for all $g \in G$ . In this paper, we investigate the structure of groups based on the assumption that every subgroup of $P \cap G^{𝒩_{p}}$ of order $p$ or 4 (if $p = 2$ ) is an $ℋ C$ -subgroup of $N_{G} (P)$ , here $P$ is a Sylow $p$ -subgroup of $G$ . Some results for a group to be $p$ -nilpotent and supersolvable are obtained and many known results are generalized.

Communicated by D. S. Passman

Keywords:

AMSC: 20D10, 20D20

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