极大子群的迹和Sylow子群的性质对可解群的影响  

Influence of Traces of Maximal Subgroups andProperties of Sylow Subgroups on Solvable Groups

作　　者：黄潇 张佳 朱丽羽 HUANG Xiao;ZHANG Jia;ZHU Liyu(School of Mathematics and Information,China West Normal University,Nanchong 637009,Sichuan Province,China;School of Mathematics and Sta tistics,Northeast Normal University,Changchun 130024,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]东北师范大学数学与统计学院,长春130024

出　　处：《吉林大学学报(理学版)》2025年第2期425-427,共3页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12371018;12001436);四川省自然科学基金(批准号:2022NSFSC1843);教育部春晖计划合作科研项目(批准号:HZKY20220567);中国博士后科学基金(批准号:2023M730545);西华师范大学基本科研业务费项目(批准号:17E091;18B032)。

摘　　要：结合Sylow子群的可补及交换条件,利用极大子群的迹的超可解性质研究若G的每个极大子群都有超可解的迹,则G是否为可解群的问题,得到了关于可解群的充分必要条件.By combining the complemented and abelian conditions of Sylow subgroups,and utilizing the supersolvable property of traces of maximal subgroups,we studied the question of whether G was a solvable group(if each maximal subgroup of G had a supersolvable trace),and obtained some sufficient and necessary conditions for solvable groups.

关 键 词：极大子群 迹 SYLOW子群 可解群 

分 类 号：O152.1[理学—数学]