有限群的F^(*)-子群与可解性  

The F^(*)-Subgroups of Finite Groups and Solubility

作　　者：何家文[1] HE Jiawen(School of General Education,Nanning University,Nanning,Guangxi Zhuang Autonomous Region,530200 China)

机构地区：[1]南宁学院通识教育学院,广西南宁530200

出　　处：《科技资讯》2022年第23期228-231,共4页Science & Technology Information

基　　金：广西高校中青年教师科研基础能力提升项目(项目编号:2019XJ0926);南宁学院教授培育工程项目(项目编号:2019JSGC09)。

摘　　要：随着有限单群分类的完成,人们通过引入新概念,采用新方法,开拓新方向等不断探讨可解群的研究。利用子群的特性确定群的可解性是可解群的重要研究方向。该文首先介绍F*-子群的概念及其性质,然后根据Sylow-子群及其极大子群、2-极大子群的子群特性,利用奇阶群可解定理和扩张理论等方法,研究了素数幂阶F*-子群对有限可解群结构的影响,并得到了可解群的若干判别准则,丰富了限可解群的理论。With the completion of the classification of finite simple groups,people continue to explore the study of solvable groups by introducing new concepts,adopting new methods and exploring new directions.Using the properties of subgroups to determine the solvability of groups is an important research direction of solvable groups.In this paper,we first introduce the concept and properties of F*-subgroups.Then,according to the properties of Sylow-subgroups and their maximal subgroups and 2-maximal subgroups,we study the influence of prime power order F*-subgroups on the structure of finite solvable groups by using the solvability theorem of odd order groups and extension theory,and obtain some criteria of solvable groups,which enrich the theory of finite solvable groups.

关 键 词：F * -子群 P-可解群 可解群 群类 

分 类 号：O152.1[理学—数学]