关于Sylow p-子群的极大子群的F-可补性对群结构的影响  

Influence of F-supplemented property of maximal subgroups of Sylow p-subgroup on the structure of groups

作　　者：高百俊 汤菊萍 高志超 宋菊 GAO Baijun;TANG Juping;GAO Zhichao;SONG Ju(School of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China;Department of Fundamental Courses,Wuxi Institute of Technology,Wuxi 214121,Jiangsu,China;School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,Hubei,China;School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,Jiangsu,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]无锡职业技术学院基础课部,江苏无锡214121 [3]华中师范大学数学与统计学院,湖北武汉430079 [4]扬州大学数学科学学院,江苏扬州225002

出　　处：《山东大学学报（理学版）》2024年第6期98-102,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12371018,11701223);江苏省高等学校基础科学(自然科学)研究项目(22KJB110024);新疆维吾尔自治区天山青年计划资助项目(2020Q023);伊犁师范大学提升学科综合实力专项自科一般项目(22xkzy19)。

摘　　要：结合群类理论,将群类S_(p)^(*)拓展到群类S_(p)^(2)^(*)和S_(p)^(3)^(*),并由此定义S_(p)^(i)^(*)-可补子群,i=1,2,3。进一步利用Sylow p-子群的极大子群的S_(p)^(i)^(*)-可补性质研究广义p-可解群的构造。Using the theory of group classes,the group classes S_(p)^(2)^(*)and S_(p)^(3)^(*)are obtained by generalizing the group class S_(p)^(*),and S*p i-supplemented subgroups are defined,where i=1,2,3.Furthermore,the structure of generalized p-solvable groups is studied by using S_(p)^(i)^(*)-supplemented property of maximal subgroups of Sylow p-subgroup.

关 键 词：Sylow p-子群 极大子群 可补子群 广义p-可解群 

分 类 号：O152.1[理学—数学]