On subgroups of the special linear group containing the special orthogonal group
type: Item
instance of: scholarly article
title: On subgroups of the special linear group containing the special orthogonal group
zbMATH Open document ID: 0572.20028
DOI: 10.1016/0021-8693(85)90045-6
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let V be an n-dimensional vector space over an arbitrary field K of characteristic not 2. Let \(O_ n\) be an orthogonal group of Witt index \(\geq 1\) and \(SL_ n\) be the special linear group over K. Let N be the normalizer of \(SL_ n\cap O_ n\) in \(SL_ n\). The main result is that N is a maximal subgroup of \(SL_ n\) for \(n\geq 3\). If \(n=2\) then a similar result holds provided the cardinality of K is at least 13.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E28
zbMATH DE Number: 3912621
zbMATH Keywords: orthogonal group
zbMATH Keywords: Witt index
zbMATH Keywords: special linear group
zbMATH Keywords: normalizer
zbMATH Keywords: maximal subgroup
author: Oliver King
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90045-6
OpenAlex ID: W2089950455
cites work: Q5795141
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description: scientific article; zbMATH DE number 3912621