S-拟正规嵌入子群与有限群的p-幂零性  

The S-Quasinormally Embedded Subgroups and p-Nilpotency of Finite Groups

作　　者：袁媛 唐康 刘建军[2] YUAN Yuan;TANG Kang;LIU Jian-jun(School of Finance, Rongzhi College of Chongqing Technology and Business University, Chongqing 401320, China;School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]重庆工商大学融智学院金融学院,重庆401320 [2]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2020年第6期1-4,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11301426);重庆市基础研究与前沿探索项目(cstc2018jcyjAX0147);中央高校基本科研业务费项目(XDJK2020B052);西南大学教改项目(2019JY096)。

摘　　要：设H是有限群G的子群.如果H的Sylow子群也分别是G的某个S-拟正规子群的Sylow子群,则称H在G中S-拟正规嵌入.利用子群的S-拟正规嵌入性给出了有限群为p-幂零群的一个充分条件,推广了已有的结论.A subgroup H of a group G is said to be S-quasinormally embedded in G,if every Sylow subgroup of H is also a Sylow subgroup of some S-quasinorml subgroup of G.In this paper,a sufficient condition for p-nilpotent groups have been obtained based on the assumption that some subgroups are S-quasinormal embedded.Our theorem is a generalization of the known results.

关 键 词：S-拟正规嵌入子群 S-拟正规子群 幂零类 P-幂零群 

分 类 号：O152.1[理学—数学]