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| 系統識別號 |
U0002-2207201000134000 |
| 中文論文名稱
|
個數小的有限群之研究 |
| 英文論文名稱
|
On finite group of small orders |
| 校院名稱 |
淡江大學 |
| 系所名稱(中) |
數學學系碩士班 |
| 系所名稱(英) |
Department of Mathematics |
| 學年度 |
98 |
| 學期 |
2 |
| 出版年 |
99 |
| 研究生中文姓名 |
楊惠迪 |
| 研究生英文姓名 |
Huei-Di Yang |
| 學號 |
697190204 |
| 學位類別 |
碩士 |
| 語文別 |
英文 |
| 口試日期 |
2010-06-22 |
| 論文頁數 |
49頁 |
| 口試委員 |
指導教授-李武炎
委員-周兆智
委員-張員榮
|
| 中文關鍵字 |
半積群
建構群
|
| 英文關鍵字 |
Semidirect product
order
|
| 學科別分類 |
學科別＞自然科學＞數學
|
| 中文摘要 |
在本論文中，利用semidirect product定理去建構一些可以做的個數小的群。但是，這並不是所有的群都可以用semidirect product去建構，所以最後做一個群的建構，不是用semidirect product這種方法建構的。首先，利用semidirect product做一些可以建構的群，之後推廣出order為p^3(p an odd prime);pq(with p and q are primes,p is smaller than q)和4p(p:prime)的群，這些特別的order的群所建構出來的形式是固定的。最後建構一個不能用semidirect product這個定理做的16個元素的群，所以我們利用Sylow's Thorem直接去建構出來。 |
| 英文摘要 |
We study the "semidirect product" of two groups H and K, which is a generalization of the direct product of H and K obtained by relaxing the requirement that both H and K be normal.
Semidirect product construction will enable us to build a "larger" group from the groups H and K.
If G contains subgroups isomorphic to H and K, in this case the subgroup H will be normal in G but the subgroup K will not necessarily be normal.
Thus, we shall be able to construct non-abelian groups even if H and K are abelian. |
| 論文目次 |
1.Background................................. 1
2.Constructions with semidirect product...... 3
Example1. ............................................ .3
(The classification of groups of order p^3, p is odd prime)
Example2.............................................. 6
(The classification of groups of order pq(p,q:prime;p is smaller than q))
Example3.............................................. 7
(The classification of groups of order 4p(p:prime;p is greater than 3))
Example4. .............................................10
(The classification of groups of order 30)
3.Constructions without semidirect product............ 13
Example:...............................................13
(The classification of groups of order 16)
4.References.......................................... 49
|
| 參考文獻 |
[1] S. Dummit and M. Foote, Abstract Algebra, 3th Ed., John Wiley and Sons, Inc., 2004
[2] W. Hungerford, Algebra, Springer Science+Business Media, LLC.,1974
[3] W. Nicholson, Introduction to Abstract Algebra, 2th Ed.,John Wiley and Sons, Inc., 1999
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| 論文使用權限 |
同意紙本無償授權給館內讀者為學術之目的重製使用，於2010-07-27公開。同意授權瀏覽/列印電子全文服務，於2010-07-27起公開。 |
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