File:NLC416-13jh009295-62074 群論.pdf

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群論   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
〔日〕圓正造著
image of artwork listed in title parameter on this page
Title
群論
Publisher
商務印書館[發行者]
Description

目錄
第一編 群的概論
第一章 置換
1 置換之定義
2 置換之結合
3 不動置換，逆置換
4 置換之連乘積，冪及其逆
5 巡迴置換
6 巡迴置換之積
7 巡迴表示法
8，9 轉換，轉換表示法
第二章 群之定義
10 置換群
11 對稱群
12 交代群
13 群之基本性質
14 元素與其結合
15 群之一般的定義
16 群之例(ⅰ)，三角群
17 群之例(ⅱ)，四面體群
18 主元素與逆元素
19 有限群
20 abel氏群
21 群之同態
第三章 約群
22 約群
23，24 傍系
25 元素之巡迴率，巡迴群
26，27 部分及其結合
第四章 共軛
28，29 共軛元素
30，31 共軛元素系
32 共軛約群
33 共軛約群系
34 自己共軛約群
35 單群，復群
36 重傍系
第五章 合同，商群
37 合同之原理
38，39 群之合同
40，41 商群
42 換位群
第六章 重複同態
43，45 重複同態
46 約群之對應
47 關於素數冪元數群之定理
第七章 組成群列
48 極大正常約群
49 組成列
50 h＃lder氏定理
51 主組成列
52 極小正常約群
53 開於商群列之項之定理
第八章 sylow及frobenius兩氏之定理
54 sylow氏定理
55 frobenius氏之擴張
第九章 群之單復，可解性
56 paq元群之可解性
67，58 frobenius氏定理
59 元數不超過100之群之單復
60 二十面體群
61 單群之元數
第二篇 置換群
第十章 可遷群
62 定義(可遷群，非遷群)
63 關於可遷群之定理
64 多重可遷群
65 對稱群與交代群
66 交代群之單純性
67 可遷重複度之限界
第十一章 非遷群
68 由可遷群以作非遷群
69 可遷系
70 非遷群之構造
71 不動文字之數
72 由正置換而成之群
第十二章 群之置換表示
73 表為正置換群者
74 正置換群為群之置換表示者
75 表示為傍系之置換群者
76 可遷群之為群之傍系置換表示者
77 表示為共軛約群(或元素)之置換群者
78 元數36，72，90者之群之複合性
79 60元單群
第十三章 可遷群之本原性及非原性
80 非原群
81 傍系置換表示之本原性及非原性
82 非原系之置換群
83 一般可遷群
84 非遷正常約群
85 非原系之選法
第十四章 可遷約群與群之可遷重複度
86 含轉換或三項巡迴置換之可遷群
87 群之有可遷約群者之可遷重複度
88 前節(2°，ⅱ)款之例
第十五章 與可遷群之各置換交換可能者之置換
89 在正置換表示時
90，91 在傍系置換表示時
92 群(〓)之可遷性及非遷性
93，94 在一般可遷群時
第十六章 自己同態，全角
95 定義
96 內外同態
97 同態群
98 正置換群之全角
99 全角之可遷重複度
100 亞巡迴群
101 一般群之全角，亞巡迴群之生成的定義
102 群之全角之即含其群者
103 特性約群
104 特性約群列
105，106 全群
107 與傍系置換表示交換可能者之置換
108 置換表示之同值
第三篇 合同群
第十七章 母式之合同乘法
109 母式
110 母式之合同，乘法之一意的條件
111，112 含最多數之母式者之集合
第十八章 母式合同群
113，114 母式合同群
115 特殊母式
116 合同群之母元素
117 〓(n，l)之母元素
118 逆母式存在之條件
119 母式之分解
120 母式合同群之分解
121 關於特殊群以及群之分解之注意
第十九章 法母式之項為素數冪者
122 母式合同群之元數(法為pμ時)
123
124 指數列
第二十章 一次變換合同群
125 一次變換
126 變換之變形
127 一次變換合同群
128 〓/〓之單純性
129 單群表
第四篇 特殊群
第二十一章 abel氏群
130 母元素，基底
131 不變系
132 abel氏群之型
133 約群之型
134 [1，1，……1]型abel氏群中之約群之數
135 abel氏群之同態群
136 sylow氏約群之同態群
137 巡迴群之同態群
第二十二章 素數冪元群之型，四元數
138 補助定理
139 含pm-1元巡迴群之pm元群
140，141 含pm2元巡迴群正常約群者之pˉm元群
142 2m元群
143 四元數，四元數群
144 四元數與二次母式之關係
145 hamilton氏群
第二十三章 母式之指針根
146，147 極，指針方程式
148 母式之正常形
第二十四章 分數變換群
149 共線變換
150 分數變換
151 有限巡迴率之條件，cayley氏變換
152 分數變換之有限群
153 有限群之種類
154 立體平畫射影
155 cayley氏變換之幾何學的意義
156 分數變換群與球之迴轉群
第五篇 群母式，群指標
第二十五章 母式之階級
157 一般母式
158 母式之生成
159 母式之階級
第二十六章 群母式
160 群母式
161 群母式之同值，簡約
162，163 既約群母式
164 同值之條件
165 正群母式，既約群母式系
第二十七章 群指針
166 群指針
167 單指針及其相關之公式
168 關於單指針之定理
169 決定單指針之方程式
170 求單指針之例
171 商之群指針
第二十八章 群指針之應用
172 pαqβ元群之可解性
173 群之指標與約群之指針之關係
174 n次n-1級可遷群
175 屬於可遷群之群母式
176 可遷群之置換與群指針之關係
177 含n次巡迴置換之n次可遷群
術語索引

Language Chinese
Publication date 民國二十三年[1934]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
館藏信息
InfoField
MG/O152/2/:1/:2
主題
InfoField
群論
中圖分類
InfoField
O152
載體形態
InfoField
2冊(630頁)

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