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系統識別號 U0026-2706201923131600
論文名稱(中文) 關於有限群中的共軛類數量
論文名稱(英文) On the number of conjugacy classes in finite groups
校院名稱 成功大學
系所名稱(中) 數學系應用數學碩博士班
系所名稱(英) Department of Mathematics
學年度 107
學期 2
出版年 108
研究生(中文) 江修毅
研究生(英文) Hsiu-Yi Chiang
學號 L16054059
學位類別 碩士
語文別 英文
論文頁數 53頁
口試委員 指導教授-黃世昌
口試委員-黃柏嶧
口試委員-蕭仁傑
中文關鍵字 有限群  共軛類數量 
英文關鍵字 finite groups  number of conjugacy classes 
學科別分類
中文摘要 在這篇論文中, 我們研究有限群的共軛類數量與有限群的階之關係. 我們特別著重在共軛類數量的界根據有限群的階. 我們會分別討論有限群以及不同類的有限群共軛類數量的上下界. 最後我們獲得了一個針對對稱群共軛類數量可能的上界.
英文摘要 In this thesis, we study the relation between the number of conjugacy classes of a finite group and its order. In particular, we are interested in the bounds for its order by the number of conjugacy classes. We will discuss the lower bounds and upper bounds for the number of conjugacy classes separately for the finite groups and further various classes of finite groups. At last, we obtain a possible upper bound for the number of conjugacy classes of symmetric groups.
論文目次 1 Introduction 6
2 Preliminaries 9
2.1 Definitions and Results . . . . . . . . . . . . . . . . . . . . . . 9
3 Lower Bounds 14
3.1 Lower bounds for finite groups . . . . . . . . . . . . . . . . . . 15
3.2 Lower bounds for solvable groups . . . . . . . . . . . . . . . . 20
3.3 Lower bounds for nilpotent groups . . . . . . . . . . . . . . . 24
3.4 Groups with order divisible by a prime p . . . . . . . . . . . . 25
4 Upper Bounds 28
4.1 Upper bounds for permutation groups . . . . . . . . . . . . . . 30
5 Groups possessing a small number of conjugacy classes 36
6 Materials and Methods 38
6.1 Permutation groups . . . . . . . . . . . . . . . . . . . . . . . . 38
6.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 39
A TABLE 44
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