SS-拟正规子群对有限群p-超可解性的影响  

Influence of SS-quasinormal subgroups on the p-supersolvability of finite groups

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)

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：《西北师范大学学报（自然科学版）》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)。

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.

关 键 词：P-子群 SS-拟正规子群 P-超可解群 极小阶反例 

分 类 号：O152.1[理学—数学]