Pólya-Ostrowski Groups and Unit Indices in Real Biquadratic Fields

The Pólya-Ostrowski group of a Galois number field K, is the subgroup Po(K) of the ideal class group Cl(K) of K generated by the classes of all the strongly ambiguous ideals of K. The number field K is called a Pólya field, whenever Po(K) is trivial. In this paper, using some results of Bennett Setzer [9] and Zantema [10], we give an explicit relation between the order of Pólya groups and the Hasse unit indices in real biquadratic fields. As an application, we refine Zantema’s upper bound on the number of ramified primes in Pólya real biquadratic fields.