具有某些特性的二极大子群对群结构的影响  

Influence of second maximal subgroups with given properties on structure of groups

作　　者：张小红[1] 刘威 王鸿志 Xiaohong ZHANG;Wei LIU;Hongzhi WANG(School of Statistics and Data Science,Ningbo University of Technology,Ningbo 315211,Zhejiang,China;College of Mathematical Science,Yangzhou University,Yangzhou 225002,Jiangsu,China;School of Mathematics,Hohai University,Nanjing 210098,Jiangsu,China)

机构地区：[1]宁波工程学院统计与数据科学学院,浙江宁波315211 [2]扬州大学数学科学学院,江苏扬州225002 [3]河海大学数学学院,江苏南京210098

出　　处：《山东大学学报（理学版）》2024年第8期15-19,27,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12371018);中央高校基本科研业务费专项资金资助(1014,423135)

摘　　要：称子群A在G中NS-可补,若存在子群B,使得G=AB,且对于A的任意正规子群X以及任意的p∈π(B),总存在B的Sylow p-子群Bp,使得XB_(p)=B_(p)X。利用特定集合中二极大子群的NS-可补、覆盖远离等性质对有限群的结构进行研究,并给出了相关群类的刻画。A subgroup A of a finite group G is said to be NS-supplemented in G,if there exists a subgroup B of G such that G=AB and whenever X is a normal subgroup of A and p∈π(B).There exists a Sylow p-subgroup Bp of B,such that XB_(p)=B_(p)X.In this paper,we explore the structure of finite groups by utilizing the properties of NS-supplement and cover-avoidance of second maximal subgroups in specific sets,and characterize the related classes of groups.

关 键 词：极大子群 二极大子群 覆盖远离性质 NS-可补 群类 

分 类 号：O152.1[理学—数学]