Pólya group in some real biquadratic fields

Abstract

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.