The influence of $\mathscr{H}$-subgroups on $p$-nilpotency and $p$-supersolvability of finite groups

Yan, Quanfu; Shen, Zhencai

doi:10.22108/ijgt.2023.135208.1806

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	The influence of $\mathscr{H}$-subgroups on $p$-nilpotency and $p$-supersolvability of finite groups
International Journal of Group Theory
مقاله 6، دوره 13، شماره 1، خرداد 2024، صفحه 55-62 اصل مقاله (415.68 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.135208.1806
نویسندگان
Quanfu Yan^* ¹؛ Zhencai Shen²
¹Department of Mathematical Sciences, Kent State University, Kent, USA
²Department of Mathematics, College of Science, China Agricultural University, Beijing, China.
چکیده
Let $G$ be a finite group. A subgroup $H$ of $G$ is an $\mathscr{H}$-subgroup in $G$ if $N_G(H)\cap H^g \leq H$ for any $g \in G$. In this article, by using the concept of $\mathscr{H}$-subgroups, we study the influence of the intersection of $O^p(G_p^*)$ and the members of some fixed $\mathcal{M}_d(P)$ on the structure of the group $G$, where $P$ is a Sylow $p$-subgroup of $G.$ Some new criteria for a group to be $p$-nilpotent and $p$-supersolvable are given and some recent results are extended and generalized.
کلیدواژه‌ها
$\mathscr{H}$-subgroup؛ weakly $\mathscr{H}$-subgroup؛ $p$-supersolvablility؛ $p$-nilpotency

مراجع
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The influence of $\mathscr{H}$-subgroups on $p$-nilpotency and $p$-supersolvability of finite groups