广义半覆盖远离子群与有限群的可解性  

On Generalized Semi-cover-avoiding of Subgroups and the Solvability of Finite Groups

作　　者：韦华全[1] 李敏 李姣 古徽龙 WEI Hua-quan;LI Min;LI Jiao;GU Hei-long(College of Mathematics and Information Science,Guangxi University,Nanning530004,China)

机构地区：[1]广西大学数学与信息科学学院

出　　处：《广西民族大学学报（自然科学版）》2019年第3期58-61,共4页Journal of Guangxi Minzu University ：Natural Science Edition

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

摘　　要：设G为有限群,H为G的子群.称H为G的广义半覆盖远离子群,如果存在G的一个主群列使得H覆盖或远离这个主群列中的每个非Frattini主因子.该文利用某些2-极大子群、极大子群的Sylow子群或3-极大子群的广义半覆盖远离性,得到有限群可解的几个充分或充要条件.Let G be a finite group and let H be a subgroup of G.H is said to be a generalized semi-cover-avoiding subgroup of G if there exists a chief series of G such that H cover or avoid every non-Frattini chief factor. By using the generalized semi-cover-avoiding properties of some 2-maximal subgroups, Sylow subgroups of maximal subgroups and 3-maximal subgroups, we present some necessary or sufficient conditions for the solvability of finite groups.

关 键 词：有限群 广义半覆盖远离子群 极大子群 SYLOW子群 可解群 

分 类 号：O152.1[理学—数学]