Finite Groups with Some Subgroups Weakly s-Permutably Embedded  

作　　者：Shouhong QIAO Yanming WANG 

机构地区：[1]School of Applied Mathematics,Guangdong University of Technology [2]Lingnan College and School of Mathematics,Sun Yat-sen University

出　　处：《Journal of Mathematical Research with Applications》2014年第5期535-542,共8页数学研究及应用（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.11201082;11171353);China Postdoctoral Science Foundation(Grant No.2013T60866);the Natural Science Foundation of Guangdong Province(Grant No.S201204007267);Outstanding Young Teachers Training Project of Guangdong Province(GrantNo.Yq2013061)

摘　　要：Let P be a Sylow p-subgroup of a group G with the smallest generator number d, where p is a prime. Denote by Md（P） = （P1, P2,..., Pd） a set of maximal subgroups of P such that φ（P） = ∩n^d=1Pn. In this paper, we investigate the structure of a finite group G under the assumption that the maximal subgroups in Md（P） are weakly s-permutably embedded in G, some interesting results are obtained which generalize some recent results. Finally, we give some further results in terms of weakly s-permutably embedded subgroups.Let P be a Sylow p-subgroup of a group G with the smallest generator number d, where p is a prime. Denote by Md（P） = （P1, P2,..., Pd） a set of maximal subgroups of P such that φ（P） = ∩n^d=1Pn. In this paper, we investigate the structure of a finite group G under the assumption that the maximal subgroups in Md（P） are weakly s-permutably embedded in G, some interesting results are obtained which generalize some recent results. Finally, we give some further results in terms of weakly s-permutably embedded subgroups.

关 键 词：finite groups weakly s-permutably embedded subgroups p-nilpotent groups p-supersolvable groups supersolvable groups. 

分 类 号：O152[理学—数学]