具有S-拟正规子群的有限群  

Finite groups with S-quasinormal subgroups

作　　者：邓燕 孟伟 DENG Yan;MENG Wei(School of Mathematics and Computer Science,Yunnan Minzu University,Kunming 650500,China;School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650550 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《云南民族大学学报（自然科学版）》2021年第4期355-358,共4页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(11761079).

摘　　要：设G是有限群,H为G的子群.如果H与G的每一个Sylow子群可置换,即对任意的P∈Syl(G),有HP=PH,则称H在G中S-拟正规.称G的素数阶子群为G的极小子群.如果G的每个极小子群在G中S-拟正规,则称G是MS-群.首先给出每个极大子群皆为MS-群的有限群必可解的新证明;然后确定了每个二极大子群皆为MS-群的有限非交换单群.Let G be a finite group.A minimal subgroup of G is a subgroup of prime order.A subgroup of G is called S-quasinormal in G if it permutes with each Sylow subgroup of G.A group G is called a MS-group if each minimal subgroup of G is S-quasinormal in G.In this paper,we give a new proof on the solvability of finite groups,all of whose maximal subgroups are MS-groups.Furthermore,we determine the finite non-abelian simple groups,all of whose second maximal subgroups are MS-groups.

关 键 词：极大子群 S-拟正规子群 可解群 单群 

分 类 号：O152.1[理学—数学]