The generation of \(\text{Sp}(\mathbb F_2)\) by transvections
type: Item
instance of: scholarly article
title: The generation of \(\text{Sp}(\mathbb F_2)\) by transvections
zbMATH Open document ID: 0345.20043
DOI: 10.1016/0021-8693(76)90105-8
author: David Callan
published in: Journal of Algebra
publication date: 1976-01-01T00:00:00Z
full work available at URL: transvections.pdf
review text: The symplectic groups \(\text{Sp}_{2n}(F)\) are generated by their transvections, and the minimal number of factors, \(t\), required to express a given \(\sigma\) in \(\text{Sp}_{2n}(F)\) as a product of (symplectic) transvections satisfies \(\text{res}\,\sigma\leq t\leq \text{res}\,\sigma +1.\) Here we determine the elements of \(\text{Sp}_{2n}(\mathbb F_2)\) for which \(t=\text{res}\,\sigma +1\), filling a gap in \textit{J. Dieudonné} [Summa Bras. Math. 3, 149--178 (1955; Zbl 0067.01201)].
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 3537933
zbMATH Keywords: symplectic groups
zbMATH Keywords: transvections
zbMATH Keywords: minimal number of factors of elements expressible as product of symplectic transvections
MaRDI profile type: Publication
OpenAlex ID: W2103905556
cites work: Q3241211
cites work: Q3227596
cites work: Q5795141
cites work: Q4043214
cites work: Products of Transvections
cites work: Q4069896
description: scientific article; zbMATH DE number 3537933