有限群的弱s-半置换子群与p-幂零性

Weakly s-semipermutable Subgroups of Finite Groups and p-nilpotence

利用弱s-半置换子群的一些基本性质研究有限群的结构,得到有限群为p-幂零群的一些充分条件.

A subgroup of a finite group is called weakly s-semipermutable in G if there is a subgroup K of G such that G=HK and H∩K≤HSSG,where HSSG is the subgroup of H generated by all those subgroup of H which are s-semipermutable in G.In this paper,the structure of finite groups in view of some basic properties of a weakly s-semipermutable subgroup are studied,and some sufficient conditions for p-nilpotence of finite groups are obtained.