关于S-半正规子群

On S-seminormal Subgroups

设G为有限群。群G的子群H称为在G中是s-半正规的,如果对任意的素数p||G|,只要(p,|H|)=1,就有PH=HP,其中,P∈Sylp(G)。本文利用子群s-的半正规性,给出了有限群的可解性与超可解性的一些新刻画。

Let G be a finite group. A subgroup of a finite group G is called s--seminormal in G if it perrnuts with every Sylow p--subgroup of G with（p, │H│ ） =1. In this paper,by using s-- semi--normal subgroups, we give some new criteria for the solvability and supersolvability of finite groups.