摘要
设G为有限群,若存在B≤G使得G=HB,且对任意p∈π(B),P∈Sy1_( p)(B),都有HP=PH,则称子群H在G中SS-拟正规.利用极小阶反例法,讨论某些p-子群SS-拟正规的有限群结构,得到p-超可解群的若干充分条件,推广了p-超可解性的部分结果.
Let G be a finite group.A subgroup H is said to be SS-quasinormal in G if there is a subgroup B of G such that G=HB,and H permutes with any Sylow p-subgroup of B for arbitrary prime p∈π(B).The structures of finite groups with SS-quasinormality of some p-subgroups are discussed by using counterexample of minimal order,and several sufficient conditions of p-supersolvable groups are obtained,which generalize some known results of p-supersolvability.
作者
高建玲
毛月梅
曹陈辰
GAO Jian-ling;MAO Yue-mei;CAO Chen-chen(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
《西北师范大学学报（自然科学版）》
CAS
2024年第2期1-5,共5页
Journal of Northwest Normal University(Natural Science)
基金
国家自然科学基金资助项目(12101339,12371021)
山西大同大学科研基金资助项目(2020K8)。
关键词
P-子群
SS-拟正规子群
P-超可解群
极小阶反例
p-subgroup
SS-quasinormal subgroup
p-supersolvable group
counterexample of minimal order
