Commutators in the symplectic group
type: Item
instance of: scholarly article
title: Commutators in the symplectic group
zbMATH Open document ID: 0628.20037
DOI: 10.1007/BF01187734
author: Rod Gow
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: We show that if \(k\) is a field of characteristic different from 2 in which \(-1\) is a square, there is a conjugacy class \(K\) of elements of order 4 in the symplectic group \(Sp(2n,k)\) with the property that each element in the group is expressible as a product of two elements in \(K\). As a consequence, each element of \(Sp(2n,k)\) is a commutator if \(k\) satisfies this condition. By way of contrast, we show that if \(-1\) is not a sum of two squares in \(k\), the central involution \(-I\) is not a commutator in \(Sp(4n+2,k)\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20F12
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 4021449
zbMATH Keywords: conjugacy classes
zbMATH Keywords: symplectic groups
zbMATH Keywords: products of two elements
zbMATH Keywords: commutators
MaRDI profile type: Publication
cites work: Isometrien von Vektorräumen. I
cites work: Commutators in the Special and General Linear Groups
cites work: Q5553361
description: scientific article; zbMATH DE number 4021449