Finite Groups with some s-Permutably Embedded and Weakly s-Permutable Subgroups
Confluentes Mathematici, Volume 5 (2013) no. 1, pp. 93-100.

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 d (P)={P 1 ,P 2 ,,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 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
Keywords: weakly $s$-permutable subgoups; $s$-permutably embedded subgroups; $p$-nilpotent groups
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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Fenfang Xie; Jinjin Wang; Jiayi Xia; Guo Zhong. Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups. Confluentes Mathematici, Volume 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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