次正规子群及其亏数对群结构的影响
发布时间：2018-12-16 12:34
【摘要】：在群理论中,人们常常通过群的子群的特征来刻画该群的结构.利用子群的次正规性来刻画群的结构是人们感兴趣的研究课题.在这篇论文中,通过对群的次正规子群及其亏数的深入研究,主要做了如下工作:首先总结和归纳了次正规子群的一些基本性质以及一些相关结果;然后介绍了次正规子群亏数的概念并给出了一些次正规子群亏数的有趣的性质;讨论了由两个子群所生成的群的有限性和可解性等问题;最后研究了次正规子群亏数与幂零类以及幂零高的大小关系,同时也给出了次正规子群亏数等于幂零类这样的有限群的例子。
[Abstract]:In group theory, the structure of a group is often characterized by the characteristics of its subgroups. It is an interesting research topic to characterize the structure of a subgroup by using its subnormality. In this paper, through the in-depth study of subnormal subgroups of groups and their deficiency numbers, the main work is as follows: firstly, some basic properties and some related results of subnormal subgroups are summarized and summarized; Then, the concept of subnormal subgroup deficiency is introduced, and some interesting properties of subnormal subgroup deficiency are given, and the finiteness and solvability of subnormal subgroup are discussed. Finally, we study the relationship between subnormal subgroup deficiency and nilpotent class and nilpotent height. At the same time, we give an example of a finite group with subnormal subgroup deficiency equal to nilpotent class.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152
本文编号：2382352
[Abstract]:In group theory, the structure of a group is often characterized by the characteristics of its subgroups. It is an interesting research topic to characterize the structure of a subgroup by using its subnormality. In this paper, through the in-depth study of subnormal subgroups of groups and their deficiency numbers, the main work is as follows: firstly, some basic properties and some related results of subnormal subgroups are summarized and summarized; Then, the concept of subnormal subgroup deficiency is introduced, and some interesting properties of subnormal subgroup deficiency are given, and the finiteness and solvability of subnormal subgroup are discussed. Finally, we study the relationship between subnormal subgroup deficiency and nilpotent class and nilpotent height. At the same time, we give an example of a finite group with subnormal subgroup deficiency equal to nilpotent class.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152
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