有限交换群的整群环的极大序及其相对K_1-群

Maximal Z-Orders of Integral Group Rings of Finite Abelian Group and Relative K_1-Group

对有限循环群和有限基本p-群讨论了它们的整群环ZG在QG中的极大Z-序Γ的具体形式,并利用这一具体形式证明了当n=1时典范同态nε∶Kn(ZG,|G|Γ)→Kn(Γ,|G|Γ是同构映射。

Let G be a finite cyclic group or elementary p-group, the structure of the maximal Z-order for their integral group rings ZG in QG is discussed. Using the results, it is proved that the canonical homomorphism εn∶Kn（ZG,｜G｜Γ）→Kn（Γ,｜G｜Γ） is an isomorphism when n=1.