# CONFLUENTES MATHEMATICI

Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups
Confluentes Mathematici, Volume 5 (2013) no. 1, p. 93-101

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 ${ℳ}_{d}\left(P\right)=\left\{{P}_{1},{P}_{2},\cdots ,{P}_{d}\right\}$ of maximal subgroups of $P$ such that ${\bigcap }_{i=1}^{d}{P}_{i}=\Phi \left(P\right)$. In the present paper, we investigate the structure of a finite group under the assumption that every member of ${ℳ}_{d}\left(P\right)$ is either $s$-permutably embedded or weakly $s$-permutable in $G$ to give criteria for a group to be $p$-supersolvable or $p$-nilpotent.

Accepted : 2013-04-16
Revised after acceptance : 2013-10-04
Published online : 2017-03-27
Classification:  20D10,  20D20
Keywords: weakly $s$-permutable subgoups; $s$-permutably embedded subgroups; $p$-nilpotent groups
@article{CML_2013__5_1_93_0,
author = {Fenfang Xie and Jinjin Wang and Jiayi Xia and Guo Zhong},
title = {Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups},
journal = {Confluentes Mathematici},
publisher = {Institut Camille Jordan},
volume = {5},
number = {1},
year = {2013},
pages = {93-101},
language = {en},
url = {https://cml.centre-mersenne.org/item/CML_2013__5_1_93_0}
}

Xie, Fenfang; Wang, Jinjin; Xia, Jiayi; Zhong, Guo. Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups. Confluentes Mathematici, Volume 5 (2013) no. 1, pp. 93-101. cml.centre-mersenne.org/item/CML_2013__5_1_93_0/

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