E-可补子群和X-拟置换子群对有限群结构的影响

发布时间：2018-02-12 00:01

本文关键词： 有限群幂零性可解性超可解性 X-拟置换 E-可补 ss-拟正规嵌入　出处：《浙江理工大学》2016年硕士论文　论文类型：学位论文

【摘要】：本文中所有群均为有限群。设H和X为群G的子群,如果存在群G的一个子群B使得()GG?N H B,且H与B及B的所有满足条件(|H|,|V|)=1的子群(Sylow子群)V X-置换,则称H在群G中X-拟置换(sX-拟置换)。群G的子群H称为在G中是E-可补的,如果存在群G的一个子群K使G=HK且eGH?K?H,其中eGH由包含在H中的G的所有s-拟正规嵌入子群生成。群G的子群H称为在G中s-拟正规嵌入的,如果对于每一个整除|G|的素数p,H的Sylow p-子群同时也是G的某个s-拟正规子群的Sylow p-子群。群G的子群H称为在G中是ss-拟正规嵌入的,如果存在G的一个子群K使G=HK且H?K在G中s-拟正规嵌入。本文主要利用X-拟置换子群(sX-拟置换子群),E-可补子群和ss-拟正规嵌入子群的性质来刻画有限群的性质和结构。本文共分六章:第一章引言,主要介绍本论文的写作背景和所取得的主要成果。第二章用于介绍本文中的一些常用的概念、符号及一些已知的基本结果。第三章主要介绍了X-拟置换子群,研究X-拟置换性对群的幂零性、可解性及超可解性的影响。第四章利用E-可补子群的性质来刻画群的幂零性和p-幂零性,以及一个群G属于给定包含所有幂零群或p-幂零群的饱和群系的条件。第五章利用ss-拟正规嵌入子群进一步研究有限群的性质和结构,得到了群G为幂零群和p-幂零群的一些条件。第六章对本文做出总结并提出与本文有关的进一步的研究问题。
[Abstract]:In this paper, all groups are finite groups. Let H and X be subgroups of group G if there is a subgroup B of group G such that G? If H satisfies all the conditions of H, B and B, then H is called X-quasi permutation and X-quasi permutation in G. The subgroup H of group G is called E- complement in G, if there exists a subgroup K of G such that G is HK and eGHH? K? Where eGH is generated by all squasinormal embedded subgroups of G contained in H. the subgroup H of group G is called squasinormal embedded in G. If the Sylow p- subgroup of every subgroup of G is also a Sylow p- subgroup of a squasinormal subgroup of G. the subgroup H of group G is said to be ss-quasinormal embedded in G, if there is a subgroup K of G such that G is HK and H? In this paper, the properties and structure of finite groups are characterized by using the properties of X-quasi permutation subgroups and ss-quasinormal embedding subgroups. This paper is divided into six chapters: chapter 1, introduction, Chapter two is used to introduce some commonly used concepts, symbols and some known basic results in this paper. Chapter three mainly introduces X-quasi permutation subgroups. The influence of X-quasi permutation on the nilpotency, solvability and supersolvability of a group is studied. In Chapter 4th, the nilpotent and pnilpotent properties of groups are characterized by the properties of E-complement subgroups. And the condition that a group G belongs to a saturated group containing all nilpotent groups or pnilpotent groups. Chapter 5th further studies the properties and structures of finite groups by using ss-quasi normal embedded subgroups. Some conditions for a group G to be a nilpotent group and a pnilpotent group are obtained. Chapter 6th summarizes this paper and puts forward further research problems related to this paper.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O152.1

【相似文献】