\(\mathrm{GL}_n (q)\) as Galois group over the rationals
type: Item
instance of: scholarly article
title: \(\mathrm{GL}_n (q)\) as Galois group over the rationals
zbMATH Open document ID: 0737.11031
DOI: 10.1007/BF01444710
author: Helmut Völklein
published in: Mathematische Annalen
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164952
review text: We prove a new criterion for realizing groups as Galois groups over the rationals. This generalizes Thompson's rigidity criterion, giving weaker conditions that include the action of the braid group on certain generating systems. Using this criterion, most of the groups \(\mathrm{GL}_n(q)\) with \(n\) even and \(n\geq 3(q-1)\) are realized as Galois groups of regular extensions of \(\mathbb{Q}(x)\). The Chevalley groups that had been realized before in this way comprised only groups over fields of prime order \(p\), or order \(p^2\).
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F12
zbMATH DE Number: 4216042
zbMATH Keywords: inverse Galois theory
zbMATH Keywords: Galois groups
zbMATH Keywords: regular extensions
zbMATH Keywords: Chevalley groups
MaRDI profile type: Publication
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OpenAlex ID: W2107303550
description: scientific article; zbMATH DE number 4216042