有限群的广义c^#-正规子群  

On Generalized c^#-subgroups of Finite Groups

作　　者：韦华全[1] 袁卫峰 周宇珍 李雪 李敏 WEI Huaquan;YUAN Weifeng;ZHOU Yuzhen;LI Xue;LI Min(College of Mathematics and Information Science, Guangxi University, Nanning Guangxi 530004, China;Dean’s Office, Guangxi University, Nanning Guangxi 530004, China)

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004 [2]广西大学教务处,广西南宁530004

出　　处：《广西师范大学学报（自然科学版）》2020年第4期54-58,共5页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11361006);广西大学科研基金(XGZ130761)。

摘　　要：设G为有限群,H为G的子群,称H为G的广义c^#-正规子群,如果存在G的正规子群K使得HK在G中正规,并且H∩K是G的CAP-子群。利用Hall子群和极大子群的广义c^#-正规性,得到有限群π-可解或可解的几个充分或充要条件。A subgroup H of a finite group G is said to be a generalized c^#-normal subgroup of G if there exists a normal subgroup K of G such that HK is normal in G and H∩K is a CAP-subgroup of G.By using the c^#-normality of some Hall and maximal subgroups,several sufficient or necessary conditions are obtained for a group to beπ-solvable or solvable.

关 键 词：有限群 广义c^#-正规子群 HALL子群 可解群 

分 类 号：O152.1[理学—数学]