On Pólya groups of some non-Galois number fields

2024/08/16 by Abbas Maarefparvar, Maarefparvar, Abbas
Mathematics · #11R21 #11R29 #11R37 #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.09019

openalex publication_date 2024/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove two conjectures proposed by Chabert and Halberstadt concerning Pólya groups of S₄-fields and D₄-fields. More generally, the latter will be proved for D_n-fields with n ≥ 4 an even integer. Further, generalizing a result of Zantema, we also prove that the pre-Pólya group of a non-Galois field of a prime degree, e.g. an A₅-field, coincides with its Pólya group.

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