p-幂零群的一些充分条件

Some Sufficient Conditions of p-nilpotent Groups

群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1,就有HK=KH。H称为s-半置换的,若对任意的p||G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G)。本文利用极小子群及极大子群的s-半置换性得到有限群为p-幂零群的一些充分条件。

Let G be a finite group. A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with （ ｜ H ｜ , ｜ K ｜ ） = 1 , and s- semipermutable if it is permutable with every Sylow p- subgroup of G with （p, ｜H｜ ） = 1. The influence of s- semipermutablity of minimal subgroups and maximal subgroups of Sylow subgroup of a finite group on its p- nilpotence are investigated.