Relative Polya Group and Polya Dihedral Extensions of Q

2018/07/09 by Ali Rajaei, Rajaei, Ali, Abbas Maarefparvar +1
Computer Science · Mathematics · #11R04 #11R29 #11R34 #11R37 #13F20 #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.NT #msc:11R04 #msc:11R29 #msc:11R34 #msc:11R37 #msc:13F20

paper · pdf · doi:10.48550/arxiv.1807.04744

openalex publication_date 2018/07/09 · arxiv created 2019/05/30 · arxiv updated 2019/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the relative Polya group for a finite extension of number fields and prove triviality of the relative Polya group for the Hilbert class field. Then we generalize our previous results on Polya S3-extensions of Q to some dihedral extensions of Q.

Citations

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

Related

• From Polya fields to Polya groups: (I) Galoisian extensions
• From Polya fields to Polya groups, (II) non-galoisian number fields
• The S-relative Pólya groups and S-Ostrowski quotients of number fields
• A note on Polya groups
• A brief survey of recent results on Pólya groups