Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups

Fenfang Xie; Jinjin Wang; Jiayi Xia; Guo Zhong

doi:10.5802/cml.4

Finite Groups with some

s

-Permutably Embedded and Weakly

s

-Permutable Subgroups

Fenfang Xie ¹ ; Jinjin Wang ¹ ; Jiayi Xia ¹ ; Guo Zhong ¹

¹ School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, Guangxi, 530023, P. R. China

Confluentes Mathematici, Tome 5 (2013) no. 1, pp. 93-100.

Résumé

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

DOI : 10.5802/cml.4

Classification : 20D10, 20D20
Mots clés : weakly $s$-permutable subgoups; $s$-permutably embedded subgroups; $p$-nilpotent groups

Affiliations des auteurs :

Fenfang Xie ¹ ; Jinjin Wang ¹ ; Jiayi Xia ¹ ; Guo Zhong ¹

¹ School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, Guangxi, 530023, P. R. China

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     title = {Finite {Groups} with some $s${-Permutably} {Embedded} and {Weakly} $s${-Permutable} {Subgroups}},
     journal = {Confluentes Mathematici},
     pages = {93--100},
     publisher = {Institut Camille Jordan},
     volume = {5},
     number = {1},
     year = {2013},
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     mrnumber = {3143613},
     language = {en},
     url = {https://cml.centre-mersenne.org/articles/10.5802/cml.4/}
}

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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, Tome 5 (2013) no. 1, pp. 93-100. doi : 10.5802/cml.4. https://cml.centre-mersenne.org/articles/10.5802/cml.4/

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