Weyl groups as Galois groups of a regular extension of the field \(\mathbb{Q}\)
type: Item
instance of: scholarly article
title: Weyl groups as Galois groups of a regular extension of the field \(\mathbb{Q}\)
zbMATH Open document ID: 0872.12001
DOI: 10.1007/BF02341873
author: Ya. N. Nuzhin
published in: Algebra and Logic
publication date: 1997-10-15T00:00:00Z
full work available at URL: https://eudml.org/doc/187727
review text: It is proved that all Weyl groups except those of type \(F_4\) are realized as Galois groups of a regular extension of the rational function field \(\mathbb{Q} (T)\). The author uses a uniform method to find a rigid rational triplet for each Weyl group (except those of types \(D_{2k}\) and \(F_4\)) and the results of \textit{G. V. Belyi} [Izv. Akad. Nauk SSSR, Ser. Mat. 43, 267-276 (1979; Zbl 0409.12012)]. Remark that the Weyl group of type \(F_4\), excluded from the main theorem, is solvable.
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 907270
zbMATH Keywords: Weyl groups
zbMATH Keywords: Galois groups
zbMATH Keywords: regular extension
zbMATH Keywords: rational function fields
zbMATH Keywords: rigid rational triplet
reviewed by: Nuria Vila
MaRDI profile type: Publication
cites work: ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
cites work: Generating sets of elements of Chevalley groups over a finite field
cites work: Generators for Simple Groups
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description: scientific article; zbMATH DE number 907270