SS-拟正规子群对有限群p-幂零性的影响  

Influence of SS-quasinormal subgroups on p-nilpotence of finite groups

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)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009 [2]宁波大学数学与统计学院,浙江宁波315211

出　　处：《山东大学学报（理学版）》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)

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.

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 

分 类 号：O152.1[理学—数学]