有限群的Coleman自同构与投射极限

发布时间：2018-07-23 20:58

【摘要】：Coleman自同构始于研究有限群在整群环的单位群中的正规化子问题,从群论的角度看,即为研究有限群的Coleman自同构是否为内自同构的问题.在本论文中,通过对有限群Coleman自同构以及投射极限的深入研究,探讨了有限p-子群及其正规化子对Coleman自同构的影响;介绍了投射极限的概念及其性质,并将其应用到自同构群的投射极限上;进一步,如果给定的群是一个投射极限,那么该群的自同构群有一个完整的刻画.本文还利用群及其自同构群的投射极限的性质给出了Coleman自同构群一个具体的构造.作为应用,给出了一些具体群的例子其Coleman自同构均为内自同构,这对研究整群环的正规化子问题具有重要意义.
[Abstract]:Coleman automorphism begins with the study of normalizing subproblems of finite groups in unit groups of integral groups. From the point of view of group theory, the problem of whether the Coleman automorphism of finite groups is inner automorphism is studied. In this paper, the effects of finite p- subgroups and their normators on Coleman automorphism are discussed by studying the finite group Coleman automorphism and projective limit, and the concept and properties of projective limit are introduced. Furthermore, if the given group is a projective limit, then the automorphism group of the group has a complete characterization. In this paper, we also give a concrete construction of Coleman automorphism group by using the properties of projective limit of group and its automorphism group. As an application, we give some examples of concrete groups whose Coleman automorphism is inner automorphism, which is of great significance to the study of normalizing subproblems of integral group rings.
【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】：O152.1

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