Generation of \(SL(n,\mathbb{Z})\) by a Jordan unipotent matrix and its transpose
type: Item
instance of: scholarly article
title: Generation of \(SL(n,\mathbb{Z})\) by a Jordan unipotent matrix and its transpose
zbMATH Open document ID: 0769.20021
DOI: 10.1016/0024-3795(93)90023-H
author: S. Singh
published in: Linear Algebra and its Applications
publication date: 1993-05-16T00:00:00Z
review text: Let \(SL(n,\mathbb{Z})\) denote the group formed by all \(n\times n\) matrices of determinant 1 with entries in \(\mathbb{Z}\). Then \(SL(n,\mathbb{Z})\) contains the \(n\times n\) Jordan unipotent block matrix \(x\) whose only eigenvalue is 1, and the transpose \(y\) of \(x\). For \(n\geq 2\) and \(n\neq 4\) the authors show that \(x\) and \(y\) generate \(SL(n,\mathbb{Z})\). In the case \(n = 4\), the matrices \(x\) and \(y\) generate a subgroup of index 8 in \(SL(n,\mathbb{Z})\).
reviewed by: Huberta Lausch
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 15B36
zbMATH DE Number: 167833
zbMATH Keywords: generators
zbMATH Keywords: Jordan unipotent block matrix
zbMATH Keywords: \(SL(n,\mathbb{Z})\)
MaRDI profile type: Publication
cites work: Q4693249
cites work: Q3993275
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description: scientific article; zbMATH DE number 167833