【摘要】：Coleman自同構始于研究有限群在整群環(huán)的單位群中的正規(guī)化子問題,從群論的角度看,即為研究有限群的Coleman自同構是否為內自同構的問題.在本論文中,通過對有限群Coleman自同構以及投射極限的深入研究,探討了有限p-子群及其正規(guī)化子對Coleman自同構的影響;介紹了投射極限的概念及其性質,并將其應用到自同構群的投射極限上;進一步,如果給定的群是一個投射極限,那么該群的自同構群有一個完整的刻畫.本文還利用群及其自同構群的投射極限的性質給出了Coleman自同構群一個具體的構造.作為應用,給出了一些具體群的例子其Coleman自同構均為內自同構,這對研究整群環(huán)的正規(guī)化子問題具有重要意義.
[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.
【學位授予單位】：青島大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O152.1

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本文編號：2140618