Construction of \(2^mS_n\)-fields containing a \(C_{2^m}\)-field
type: Item
instance of: scholarly article
title: Construction of \(2^mS_n\)-fields containing a \(C_{2^m}\)-field
zbMATH Open document ID: 0917.12002
author: Teresa Crespo
published in: Journal of Algebra
publication date: 1998-12-13T00:00:00Z
review text: The author considers the embedding problem given by the epimorphism \(2^m{\mathfrak S}_n^+\to{\mathfrak S}_n\). Here \({\mathfrak S}_n\) denotes the symmetric group on \(n\) letters and \({\mathfrak S}_n^+\) is one of the two double covers of \({\mathfrak S}_n\). She obtains a criterion for the solvability of the embedding problem and a method of computation of the solutions by reducing to an embedding problem with kernel of order 2. Under certain conditions on the ground field the obstruction is given in terms of quaternion algebras and Hasse-invariants of the trace form of a subextension. The proofs are based on the author's previous work and results of Fröhlich, Quer, Serre and Swallow.
Mathematics Subject Classification ID: 12F12
zbMATH DE Number: 1211662
zbMATH Keywords: solvability of the embedding problem
zbMATH Keywords: obstruction
reviewed by: Martin Epkenhans
MaRDI profile type: Publication
full work available at URL: jabr.1997.7232
OpenAlex ID: W126381469
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DOI: 10.1006/JABR.1997.7232
description: scientific article; zbMATH DE number 1211662