有限群可解的若干充分条件  

Some Sufficient Conditions on Solvability of Finite Groups

作　　者：康旺强[1] 覃雪清 卢家宽 KANG Wang-qiang;QIN Xue-qing;LU Jia-kuan(Department of Economics and Management,Lijiang College,Guangxi Normal University,Guilin Guangxi 541006,China;Institute of Information Technology,Guilin University of Electronic Technology,Guilin Guangxi 541004,China;School of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)

机构地区：[1]广西师范大学漓江学院,经济与管理学院,广西桂林541006 [2]桂林电子科技大学信息科技学院,广西桂林541004 [3]广西师范大学数学与统计学院,广西桂林541006

出　　处：《西南师范大学学报（自然科学版）》2021年第2期4-7,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11861015);广西自然科学基金项目(2020GXNSFAA238045);广西高校中青年教师科研基础能力提升项目.

摘　　要：证明了有限可解群的若干性质:若有限群G的非正规非交换极大子群皆共轭,则G是可解群;若有限群G中非正规子群的共轭类个数不超过极大子群的共轭类个数,则G是可解群;设G是有限群,若G的非幂零极大子群的指数为素数或素数的平方,则G是可解群.In this paper,some sufficient conditions on solvability of finite groups obtained:If all non-normal non-abelian subgroups of a finite group G are conjugate,then G is solvable;If the number of conjugacy classes of non-normal subgroups of a finite group G is no more than thenumber of conjugacy classes of maximal subgroups of G,then G is solvable;If the indexs of its non-nilpotent maximal subgroups of G are prime or the square of prime,then G is solvable.

关 键 词：可解群 极大子群 非正规子群 非交换子群 

分 类 号：O152.1[理学—基础数学]