The Galois group of a radical extension of the rationals
type: Item
instance of: scholarly article
title: The Galois group of a radical extension of the rationals
zbMATH Open document ID: 0717.12002
DOI: 10.1007/BF02568433
author: Eliot T. Jacobson
author: William Yslas Vélez
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155500
review text: Die Autoren geben eine explizite Beschreibung der Galoisgruppe eines irreduziblen Binoms \(X^ n-a\in \mathbb Q[X]\) als volle Untergruppe des semidirekten Produkts \(G=(\mathbb Z/n\mathbb Z)\rtimes (\mathbb Z/n\mathbb Z)^{\times}\) (eine Untergruppe von \(G\) heißt voll, wenn ihre Projektionen auf beide Faktoren surjektiv sind). Ferner wird gezeigt, daß jede volle Untergruppe von \(G\) Galoisgruppe eines geeigneten irreduziblen Binoms über \(\mathbb Q\) ist.
reviewed by: Franz Halter-Koch
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 11R20
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 4181472
zbMATH Keywords: Galois group
zbMATH Keywords: splitting field
zbMATH Keywords: irreducible binomial
MaRDI profile type: Publication
cites work: The lattice of subfields of a radical extension
cites work: On the degree of the splitting field of an irreducible binomial
cites work: The torsion group of a radical extension
cites work: Fields arithmetically equivalent to a radical extension of the rationals
cites work: Q5576154
cites work: On normal binomials
cites work: Several results on radical extensions
cites work: Q4117916
cites work: Q5587110
OpenAlex ID: W2010331547
description: scientific article; zbMATH DE number 4181472