Products of cyclic similarity classes in the groups \(\text{GL}_n(F)\)
type: Item
instance of: scholarly article
title: Products of cyclic similarity classes in the groups \(\text{GL}_n(F)\)
zbMATH Open document ID: 0806.20037
DOI: 10.1016/0024-3795(94)90192-9
author: Arieh Lev
published in: Linear Algebra and its Applications
publication date: 1994-08-15T00:00:00Z
review text: Let \(\text{SL}_n(F)\) and \(\text{PSL}_n(F)\) denote the special linear and the projective special linear group, respectively. Assume \(|F|\geq 4\). The author shows that the group \(G=\text{PSL}_n(F)\) has a conjugacy class \(C\) such that \(C^2=G\). Further, if \(A\in\text{SL}_n(F)\), then \(A\) is a product of three cyclic unipotent matrices, if \(A\) is nonscalar, then it is a product of two cyclic unipotent matrices. These results are obtained as consequences of a factorization of any nonscalar matrix into two cyclic matrices having prescribed Jordan canonical form.
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 614118
zbMATH Keywords: products of cyclic unipotent matrices
zbMATH Keywords: projective special linear groups
zbMATH Keywords: conjugacy classes
zbMATH Keywords: factorizations
zbMATH Keywords: Jordan canonical form
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90192-9
OpenAlex ID: W2013353037
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description: scientific article; zbMATH DE number 614118