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系統識別號 U0026-0507201922400600
論文名稱(中文) 共軛類對有限群的影響
論文名稱(英文) On the influence of conjugacy class 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) 任靜宜
研究生(英文) Ching-Yi Jen
學號 L16064038
學位類別 碩士
語文別 英文
論文頁數 32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 共軛類大小  質數次方指數元素  q-Baer 群  normal p-complement 
英文關鍵字 conjugacy class size  element of prime-power index  q-Baer group  normal p-complement 
學科別分類
中文摘要 在這篇論文中,我們列出一些與元素的指數(index)相關的結果。首先是和指數為質數次方的元素有關的結果,包含單一性(simplicity),normal p-complement 的存在性,以及一個元素擁有質數次方的指數的充分條件。接著我們舉一些例子說明滿足 order 為質數次方的元素都有質數次方指數這種條件的群還有 q-Baer 群。最後列出由元素的指數所推導出的和群的可解性(solubility)有關的結果。
英文摘要 In this thesis, we show some results about index of an element. We first show results about elements of prime-power indices, which include simplicity, the existence of normal p-complements, and sufficient conditions for an element to have prime-power index. Next, we give some examples of groups such that elements of prime-power order have prime-power indices, and q-Baer groups. The last part, we show some results that the indices of elements in a group can imply the solubility of it.
論文目次 1 Introduction 1
2 De finitions and Basic Results 3
2.1 De finitions 3
2.2 Basic Results 4
3 Elements of Prime-power Indices 7
3.1 Nonsimplicity 7
3.2 Normal p-complement 8
3.3 Sufficient Conditions for Elements to Have Prime
-Power Index 14
4 Elements of Prime-power Order Having Prime-power Indices and the q-Baer Group 16
4.1 Characterisation by Baer 16
4.2 q-Baer Group 17
5 Solubility 20
5.1 Index Not Divisible by p^2 20
5.2 Square-free Index 24
Notation 27
Index 29
Bibliography 30
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