模群代数中的酉单位
Unitary units in modular group algebras
摘要：
设p是素数，K是特征为p的域，G是局部有限p-群，KG是群代数，V是KG的增广单位群. G的反自同构g \mapsto g^{-1}线性扩张到KG;这个扩张使得V是集不变的，并且它对V的限制后面跟着v \mapsto v^{-1}存在V的一个自同构。我们的第一个定理描述了这个子群在V中正规的K和G。对于G中的每个元素g，让\bar{g}表示g的不同幂的和（以KG为单位）。元素1+（g-1）h \bar{g}与g，h \in G是KG的双环单元。我们的第二个定理描述了所有双环单位都是幺正的K和G。
英文摘要：
Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this extension leaves V setwise invariant, and its restriction to V followed by v\mapsto v^{-1} lives an automorphism of V. The elements of V fixed by this automorphism are called unitary; they form a subgroup. Our first theorem describes the K and G for which this subgroup is normal in V. For each element g in G, let \bar{g} denote the sum (in KG) of the distinct powers of g. The elements 1+(g-1)h\bar{g} with g,h\in G are the bicyclic units of KG. Our second theorem describes the K and G for which all bicyclic units are unitary.
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