有限内MSS-群的分类

A Classification of Finite Minimal Non-MSS-Groups

有限群G的子群H称为G的s-半置换子群,若H与G的每个满足条件(p,|H|)=1的Sylow p-子群可置换.若有限群G的每个极小子群和4阶循环子群都在G中s-半置换,则称G为MSS-群.给出群G的每个真子群是MSS-群但G本身不是MSS-群的分类.

A subgroup H of a finite group G is called s-semipermutable in G if HG_p = G_pH for any Sylow p-subgroup G_p of G with（p,｜H｜） = 1.A finite group G is called an MSS-group if all minimal subgroups and cyclic subgroups with order 4 of G are s-semipermutable in G.In this paper,we classify these groups which are not MSS-groups but whose proper subgroups are all MSS-groups.