Explicit construction of \(2S_ n\) Galois extensions
type: Item
instance of: scholarly article
title: Explicit construction of \(2S_ n\) Galois extensions
zbMATH Open document ID: 0704.11044
DOI: 10.1016/0021-8693(90)90223-B
author: Teresa Crespo
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: The author considers the construction of explicit solutions to the embedding problems given by 2G\(\to G\simeq Gal(L/K)\), where G is a subgroup of the symmetric group \(S_ n\), 2G is the preimage of G in either of the two stem covers of \(S_ n\); K is a field of characteristic different from 2 and L/K is a Galois extension with Galois group G. The author reduces this embedding problem to an \(A_ n\)-type embedding problem, where \(\tilde A_ n\) is the double cover of the alternating group \(A_ n\). Then, she uses the explicit solution obtained in her previous paper [J. Algebra 127, 452-461 (1989; see the preceding review)] to reach an explicit formula for the present embedding problem. Moreover, an alternative method of resolution is given in order to simplifie effective computations, in the case \(2^+S_ n\).
reviewed by: Nuria Vila
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F10
zbMATH DE Number: 4154558
zbMATH Keywords: embedding problems
zbMATH Keywords: symmetric group
zbMATH Keywords: Galois extension
zbMATH Keywords: Galois group
zbMATH Keywords: alternating group
MaRDI profile type: Publication
cites work: Erratum to: ``Explicit construction of \(\widetilde A_ n\) type fields''
cites work: The Witt invariant of the form \(\text{Tr}(x^ 2)\)
cites work: On stem extensions of \(S_ n\) as Galois group over number fields
full work available at URL: 0021-8693(90)90223-b
OpenAlex ID: W1976467152
description: scientific article; zbMATH DE number 4154558