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Paper   IPM / M / 16695
School of Mathematics
  Title:   Polya group in some real biquadratic fields
  Author(s):  Abbas Maarefparvar
  Status:   Published
  Journal: J. Number Theory
  Vol.:  228
  Year:  2021
  Pages:   1-7
  Supported by:  IPM
  Abstract:
For a Galois extension K/\mathbbQ, Pólya group of K coincides with subgroup of strongly ambiguous ideal classes of K, which is controlled by ramification and Galois cohomology of units, and a number field with trivial Pólya group is called a Pólya field. In this paper, using Setzer's result [] on the first cohomology group of units in real biquadratic fields, we describe structure of Pólya group for an infinite family of real biquadratic fields with 5 ramification and no quadratic Pólya subfield. Moreover, in this family order of Pólya group is same as the Hasse unit index.

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