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| 研究生： |
張弼程 |
|---|---|
| 論文名稱： |
Zassenhaus Conjecture for Some Metabelian Groups |
| 指導教授： | 劉家新 |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2010 |
| 畢業學年度： | 98 |
| 語文別： | 英文 |
| 論文頁數： | 27 |
| 英文關鍵詞： | integral group rings, Zassenhaus Conjecture, torsion units |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：127 下載：8 |
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在1960 年代中期， 關於 integral group rings 中的 torsion units 及 finite subgroups，Zassenhaus 提出了三個猜想。
其中最強的一個猜想（ZC-3）如此敘述：
如果 H 是 V(ZG) 中的有限子群， 則 H 會和 G 裡的一個子群在 QG 中共軛。
雖然此一猜想已有反例，但依然具有研究價值。在此篇論文中我們將證明：
若一有限群G包含一個 normal abelian Sylow p-subgroup A，並且G/ A 是abelian，則G 滿足（ZC-3）。
In the 1960's, H. Zassenhaus made three conjectures about torsion units and finite subgroups of the units in integral group rings.
The strongest one (ZC-3) states:
If H is a finite subgroup of V(ZG), then H is conjugate to a subgroup of G in QG.
In this thesis, we prove that if G contains a normal abelian Sylow p-subgroup A with G/ A abelian, then (ZC-3) holds for G.
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