On the smallest discriminants of quaternionic fields
type: Item
instance of: scholarly article
title: On the smallest discriminants of quaternionic fields
zbMATH Open document ID: 0854.11057
DOI: 10.1007/BF01268925
published in: Archiv der Mathematik
publication date: 1996-11-22T00:00:00Z
review text: Let \(G\) be the quaternion group of order \(4n\), and let \(N\) be a normal extension of the field \(\mathbb{Q}\) of rational numbers with Galois group isomorphic to \(G\). This paper deals with the discriminants of \(N\), particularly when \(n\) is a prime number. We find the smallest discriminants (real and imaginary) when \(n= 2, 3\) or 5. In addition we determine also all fields \(N\) with \(d_N\leq 10^{16}\) if \(n=2\) and all fields \(N\) with \(d_N\leq 10^{20}\) if \(n=3\).
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R21
zbMATH DE Number: 938582
zbMATH Keywords: quaternion extension
zbMATH Keywords: character of a finite group
zbMATH Keywords: Artin's conductor
zbMATH Keywords: quaternion group
zbMATH Keywords: smallest discriminants
author: Soun-Hi Kwon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 938582