假定 G 是一个有限的组， H 是 G 的亚群。我们说 H 是在 G 的 s-semipermutable 如果为 G 与的任何 Sylow p 亚群 G p 的 H G p = G p H (p， |H|)= 1。我们在有限的组的结构上调查 s-semipermutable 亚群的影响。一些最近的结果被概括并且统一。关键词 s-semipermutable 亚群 - 概括恰当的亚群 - p-nilpotent 组 - 浸透的形成先生(2000 ) 题目分类 20D10 - 20D20 由中国(资助号码 10871210 ) 的国家自然科学基础支持了，广东省(资助号码 06023728 )
Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md(P) = {P1,...,Pd}, such that di=1 Pi = Φ(P), the Frattini subgroup of P. In this paper, we will show that if each member of some fixed Md(P) is either p-cover-avoid or S-quasinormally embedded in G, then G is p-nilpotent. As applications, some further results are obtained.
Xuan Li HE1,2, Yan Ming WANG3 1. Department of Mathematics, Zhongshan University, Guangdong 510275, P. R. China
