A note on Polya groups

2023/02/15 by Étienne Emmelin, Emmelin, Étienne
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.07977

openalex publication_date 2023/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K/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.

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