From Polya fields to Polya groups: (I) Galoisian extensions

Abstract

The Pólya group of a number field K is the subgroup of the class group of K generated by the classes of the products of the maximal ideals with same norm. A Pólya field is a number field whose Pólya group is trivial. Our purpose is to start with known assertions about Pólya fields to find results concerning Pólya groups. This first paper inspired by Zantema's results focuses on the Pólya group of the compositum of two galoisian extensions of Q.