Remarks on the generation of orthogonal groups over finite fields
type: Item
instance of: scholarly article
title: Remarks on the generation of orthogonal groups over finite fields
zbMATH Open document ID: 0834.20051
author: Andrew G. Earnest
author: R. A. Catalpa
author: U. S. Schmidt
author: G. T. Stewart
published in: Journal of Algebra
publication date: 1996-03-21T00:00:00Z
review text: The authors show: Let \(O(V)\) be the orthogonal group of a nonsingular quadratic space of dimension \(n\) over a finite field \(K\). Then \(O(V)\) is generated by two elements. In addition, if \(\text{char }K=2\) and \(|K|\neq 2\), then \(O(V)\) is generated by \(n+1\) symmetries. The present paper deals mainly with the cases \(\text{char }K=2\) and \(|K|=3\) and relies for the other cases on results by \textit{H. Ishibashi} and \textit{A. G. Earnest} [in J. Algebra 165, 164-171 (1994; Zbl 0805.20039)].
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 815927
zbMATH Keywords: generated by symmetries
zbMATH Keywords: orthogonal groups
zbMATH Keywords: nonsingular quadratic spaces
zbMATH Keywords: finite fields
zbMATH Keywords: generated by two elements
MaRDI profile type: Publication
full work available at URL: jabr.1995.1261
OpenAlex ID: W2068471867
DOI: 10.1006/JABR.1995.1261
description: scientific article; zbMATH DE number 815927