摘要
设G为有限群,子群H称为在G中SS-拟正规,若存在B≤G满足G=HB,且对所有p∈π(B),P∈Syl_(p)(B),有HP=PH皆成立。借助准素数子群的SS-拟正规性研究有限群结构,利用对|G|的归纳法及极小阶反例法,给出了p-幂零群若干新的判别准则。
Let G be a finite group.A subgroup H is called SS-quasinormal in G if there is a subgroup B of G such that G=HB,and HP=PH holds for all prime p∈π(B)and P∈Syl_(p)(B).The structures of finite groups with SS-quasinormality of primary subgroups are studied.Some new criteria of p-nilpotent group are given by using induction on the order of G and counterexample of minimal order.
作者
高建玲
毛月梅
曹陈辰
Jianling GAO;Yuemei MAO;Chenchen CAO(School of Mathematics and Statistics,Shanxi Datong University,Datong 037009,Shanxi,China;School of Mathematics and Statistics,Ningbo University,Ningbo 315211,Zhejiang,China)
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2024年第8期9-14,共6页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金青年科学基金资助项目(12101339)
国家自然科学基金资助项目(12371021)
山西大同大学科研基金资助项目(2020K8)
关键词
SS-拟正规子群
P-幂零群
P-超可解群
归纳法
极小阶反例
SS-quasinormal subgroup
p-nilpotent group
p-supersolvable group
induction
counterexample of minimal order
