具有S-拟正规子群的有限群

Finite groups with S-quasinormal subgroups

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.