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Pólya group in some real biquadratic fields
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-05-28 , DOI: 10.1016/j.jnt.2021.04.012
Abbas Maarefparvar

For a Galois extension K/Q, Pólya group Po(K) of K coincides with the subgroup of strongly ambiguous ideal classes of K, which is controlled by ramification and Galois cohomology. Using Setzer's result [9] on the first cohomology group of units in the real biquadratic fields, we describe the structure of Po(K) for an infinite family of real biquadratic fields K with five ramifications and no quadratic Pólya subfield. Moreover, #Po(K) in this family is the same as the Hasse unit index.



中文翻译:

一些真正的双二次域中的 Pólya 群

对于伽罗瓦扩展 /, 波利亚集团 Ø()ķ具有强烈暧昧理想类的亚组一致ķ,这是由分枝和伽罗瓦上同调控制。使用 Setzer 在实际双二次域中的第一个上同调组上的结果 [9],我们描述了Ø()对于具有五个分支且没有二次 Pólya 子域的无限实双二次场K族。而且,#Ø() 在这个族中与 Hasse 单位指数相同。

更新日期:2021-05-28
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