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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2011, том 12, выпуск 1, страницы 20–27 (Mi adm55)

Эта публикация цитируется в 1 статье

RESEARCH ARTICLE

The influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency of finite groups

Changwen Li

School of Mathematical Science, Xuzhou Normal University, Xuzhou, Jiangsu, 221116, P.R. China

Аннотация: Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is said to be $s$-permutably embedded in $G$ if for each prime $p$ dividing $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; $H$ is called weakly $s$-permutably embedded in $G$ if there are a subnormal subgroup $T$ of $G$ and an $s$-permutably embedded subgroup $H_{se}$ of $G$ contained in $H$ such that $G=HT$ and $H\cap T\leq H_{se}$. We investigate the influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency of finite groups.

Ключевые слова: weakly $s$-permutably embedded subgroups; $p$-nilpotent; maximal subgroup; 2-maximal subgroup.

MSC: 20D10, 20D20

Поступила в редакцию: 13.07.2010
Исправленный вариант: 29.09.2011

Язык публикации: английский



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