有限群的可解性与其部分极大子群的SS-可补性  

The Solvability of Finite Groups and the SS-Supplementarity of Partial Maximal Subgroups

作　　者：袁媛 常健 刘建军[2] YUAN Yuan;CHANG Jian;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4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).

摘　　要：设H是有限群G的子群,如果存在G的一个子群K,使得G=HK且H∩K在K中S-拟正规,则称H在G中SS-可补.利用部分极大子群的SS-可补性给出了有限群可解和p-可解的一些充分条件.A subgroup H of a group G is said to be SS-supplemented in G,if there exists a subgroup K of G such that G=HK and H∩K is S-quasinormal in K.In this paper,some sufficient conditions for solvability and p-solvability of finite groups are obtained by using the SS-supplementarity of partial maximal subgroups.

关 键 词：SS-可补子群 极大子群 可解群 P-可解群 

分 类 号：O152.1[理学—数学]