A note on Polya groups

Let $K\mathrm{/}\mathbf{Q}$ be a finite Galois extension. The Pólya group of $K$ is the subgroup of the class group $Cl(K)$, generated by the classes of ambiguous ideals of $K$. In this note, among other results, we prove that every finite abelian group is isomorphic to the Pólya group of a number field.