The elements of the orthogonal group \(\Omega_ n(V)\) as products of commutators of symmetries
type: Item
instance of: scholarly article
title: The elements of the orthogonal group \(\Omega_ n(V)\) as products of commutators of symmetries
zbMATH Open document ID: 0859.20038
author: Alexander J. Hahn
published in: Journal of Algebra
publication date: 1997-04-10T00:00:00Z
review text: Let \(F\) be a field of characteristic not 2 and let \(V\) be an \(n\)-dimensional nondegenerate quadratic space over \(F\). Every element in the commutator subgroup \(\Omega_n(V)\) of the orthogonal group \(O_n(V)\) is a product of commutators of symmetries. The author shows that, if \(F\) is a local field, every element in \(\Omega_n(V)\) is a product of \([n/2]\) such commutators, except a few elements for which \([n/2]+1\) commutators are required.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 51F25
Mathematics Subject Classification ID: 20G25
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F12
zbMATH DE Number: 941274
zbMATH Keywords: commutator subgroups
zbMATH Keywords: orthogonal groups
zbMATH Keywords: products of commutators of symmetries
zbMATH Keywords: local fields
MaRDI profile type: Publication
full work available at URL: jabr.1996.0292
OpenAlex ID: W1986094523
DOI: 10.1006/JABR.1996.0292
description: scientific article; zbMATH DE number 941274