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 在1960年代中期， 關於 integral group rings 中的 torsion units 及 finite subgroups， H. 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 integral group ring ZG 裡係數和為 1 的 unit group 的有限子群， 則 H 會和 G 裡的一個子群在 QG 裡共軛。這篇論文裡， 我們要證明的是 ZC-3 對個數為 p^2q 的群皆成立， 其中 p, q 為相異質數。
 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 the unit group of augmentation 1 in the integral group ring ZG, then H is conjugate to a subgroup of G in QG.In this thesis, we prove that ZC-3 holds for groups of order p^2q, where p, q are distinct primes.
 Contents1 Introduction 12 Preliminary 42.1 Universal Property . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Representations and Characters . . . . . . . . . . . . . . . . . 52.3 Torsion Units and Finite Subgroups . . . . . . . . . . . . . . . 93 Some Observations 123.1 Groups of Order p2q . . . . . . . . . . . . . . . . . . . . . . . 123.2 Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Some Known Results and Simple Cases 205 Representations and Some Reductions 236 Main result 27
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