Zassenhaus Conjecture for Some Metabelian Groups
Abstract
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.
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.
Description
Keywords
integral group rings, Zassenhaus Conjecture, torsion units