Pólya-Ostrowski Group and Unit Index in Real Biquadratic Fields (2108.01904v3)

Abstract: For a Galois number field $K$, P\'olya-Ostrowski group of $K$ is the subgroup of the ideal class group of $K$ generated by all strongly ambiguous ideal classes. $K$ is called a P\'olya field, whenever its P\'olya group is trivial. In this paper, using some results in \cite{Bennett, Zantema}, we give an explicit relation between order of P\'olya groups and Hasse unit indices in real biquadratic fields.