On p-Cover-Avoid and S-Quasinormally Embedded Subgroups in Finite Groups  

作　　者：Xuan Li HE1,2, Yan Ming WANG3 1. Department of Mathematics, Zhongshan University, Guangdong 510275, P. R. China 2. College of Mathematics and Information Science, Guangxi University, Guangxi 530004, P. R. China 3. Lingnan College and Department of Mathematics, Zhongshan University, Guangdong 510275, P. R. China 

出　　处：《Journal of Mathematical Research and Exposition》2010年第4期743-750,共8页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10571181);the National Natural Science Foundation of Guangdong Province (Grant No.06023728) ;the Specialized Research Fund of Guangxi University (Grant No.DD051024)

摘　　要：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.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.

关 键 词：p-cover-avoid subgroup S-quasinormally embedded subgroup p-nilpotent group. 

分 类 号：O152.1[理学—数学]