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

2018/05/29 by Jean-Luc Chabert, Chabert, Jean-Luc · 2 citations
Mathematics · #11R04 (Primary) 11R32 (Secondary) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1805.11585

openalex publication_date 2018/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Polya 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 Polya field is a number field whose Polya group is trivial. Our purpose is to start with known assertions about Polya fields to find results concerning Polya groups. This first paper inspired by Zantema's results focuses on the Polya group of the compositum of two galoisian extensions of Q.

Cited by

• Absolutely Abelian Hilbert Class Fields and ℓ-torsion conjecture
• Relative Polya Group and Polya Dihedral Extensions of Q

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