【作者】 郭青宏；

【导师】 何宣丽；

【作者基本信息】 广西大学 ， 数学， 2021， 硕士

【摘要】 在有限群理论的研究中,主要的研究内容之一是对有限群的结构进行刻画.目前,使用子群的嵌入性质来研究有限群的结构一直都是国内外学者研究的热门课题,并且得到了许多有意义的成果.本文主要研究弱HC-嵌入子群和SS-可补子群对有限群结构的影响.全文共分为四章.第一章主要介绍本文的研究背景及现状.第二章主要介绍本文涉及的一些基本概念和引理.第三章研究弱HC-嵌入子群对有限群结构的影响.我们主要利用Sylow子群的某些固定阶层子群的弱HC-嵌入性和某些局部子群的p-幂零性来刻画有限群的p-超可解性和p-幂零性.第四章研究SS-可补子群对有限群结构的影响.首先分别利用Sylow子群的2-极小子群和2-极大子群得到A4-自由群是p-幂零群的充分条件;其次因为2是特殊的素数,我们利用SS-可补子群给出了有限群是2-幂零的一个充分条件;然后将SS-可补子群限制在局部子群NG(P)中来研究有限群的p-幂零性;接着给出某些饱和群系的相关结果;最后刻画了SS-可补群.更多还原

【Abstract】 In the study of finite group theory,one of the main research contents is to characterize the structure of finite group.At present,using the embedding property of subgroups to study the structure of finite groups has always been a hot topic for scholars,and many meaningful results have been obtained.In the thesis,we study the influence of weakly HC-embedded subgroups and SS-supplemented subgroups on the structure of finite groups.The whole dissertation is divided into four chapters.Chapter 1,we introduce the research background and development status of this thesis.Chapter 2,we introduce some basic concepts and lemmas related to this dissertation.Chapter 3,to study the influence of weakly HC-embedded subgroups on the structure of finite groups,the p-supersolvability and p-nilpotency of finite groups are described by using the weakly HC-embeddedness of some fixed order subgroups of Sylow subgroups and p-nilpotency of some local subgroups.Chapter 4,to study the influence of SS-supplemented subgroups on the structure of finite groups.Firstly,using 2-minimal and 2-maximal subgroups of Sylow subgroups get A4-free groups are p-nilpotent,respectively;secondly,be-cause 2 is a special prime number,we use SS-supplemented subgroups to give a sufficient condition that the finite groups are 2-nilpotent;then SS-supplemented subgroups are restricted to the local subgroup NG(P)to study the p-nilpotency of finite groups;and next the correlation results of some saturated formations are given;finally,the SS-supplemented group is characterized.更多还原