摘要
Shlyk定理说明任一有限非可解群的所有非正规的非幂零极大子群的交必幂零。本文给出Shlyk定理一个新的证明,并证明了任一有限非可解群的所有非幂零极大子群的交必等于它的Frattini子群。
The theorem of Shlyk indicates that the intersection of all nonnormal nonnilpotent maximal subgroups of a finite nonsolvable group is nilpotent.In this paper,a new proof of Shlyk＇s theorem is given.Moreover,it is proved that the intersection of all nonnilpotent maximal subgroups of a finite nonsolvable group must be equal to its Frattini subgroup.
出处
《广西师范大学学报（自然科学版）》
CAS
北大核心
2012年第1期22-24,共3页
Journal of Guangxi Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(10871032)
中国博士后科学基金资助项目(201104027)
“Agencija za raziskovalno dejavnost Republike Slovenije”,proj.mladi raziskovalci
“Agencija za raziskovalno dejavnost Republike Slovenije”,research program(P1-0285)
关键词
有限群
非幂零极大子群
可解群
finite group
nonnilpotent maximal subgroup
solvable group
