Bounds on orders of finite subgroups of \(\text{PGL}_n(K)\)
type: Item
instance of: scholarly article
title: Bounds on orders of finite subgroups of \(\text{PGL}_n(K)\)
zbMATH Open document ID: 0919.20029
author: Eli Aljadeff
author: Jack Sonn
published in: Journal of Algebra
publication date: 1999-06-30T00:00:00Z
review text: Let \(B(K,n)\) and \(B'(K,n)\) denote the statements that there is a bound on the orders of the finite nonmodular subgroups of \(\text{GL}_n(K)\) and \(\text{PGL}_n(K)\), respectively. The authors show that \(B(K,n)\) is equivalent to \(B'(K,n)\) for all \(n\geq 2\). They also characterize \(B(K,n)\) in terms of cyclotomic extensions of \(K\) and they apply their results to the multiplicative subgroups of finite dimensional central simple \(K\)-algebras.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 1247582
zbMATH Keywords: order bounds
zbMATH Keywords: finite subgroups
zbMATH Keywords: projective general linear groups
MaRDI profile type: Publication
full work available at URL: jabr.1998.7551
OpenAlex ID: W2047582903
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DOI: 10.1006/JABR.1998.7551
description: scientific article; zbMATH DE number 1247582