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Fenfang Xie; Jinjin Wang; Jiayi Xia; Guo Zhong
Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups
Confluentes Mathematici, 5 no. 1 (2013), p. 93-101, doi: 10.5802/cml.4
Article PDF | Analyses MR 3143613
Class. Math.: 20D10, 20D20
Mots clés: weakly $s$-permutable subgoups; $s$-permutably embedded subgroups; $p$-nilpotent groups

Résumé - Abstract

Let $G$ be a finite group, $p$ the smallest prime dividing the order of $G$ and $P$ a Sylow $p$-subgroup of $G$ with the smallest generator number $d$. There is a set $\mathcal{M}_d(P) = \lbrace P_1, P_2, \cdots , P_d\rbrace $ of maximal subgroups of $P$ such that $\bigcap ^d _{i=1}P_i=\Phi (P)$. In the present paper, we investigate the structure of a finite group under the assumption that every member of $\mathcal{M}_d(P)$ is either $s$-permutably embedded or weakly $s$-permutable in $G$ to give criteria for a group to be $p$-supersolvable or $p$-nilpotent.

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