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.
作者
康旺强
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)
出处
《西南师范大学学报（自然科学版）》
CAS
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.
关键词
可解群
极大子群
非正规子群
非交换子群
solvable group
maximal subgroup
non-normal subgroup
non-abelian subgroup
