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 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.

Received : 2012-05-10
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
     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 = {}
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.

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