Linear groups containing a root subgroup
type: Item
instance of: scholarly article
title: Linear groups containing a root subgroup
zbMATH Open document ID: 0874.20031
DOI: 10.1007/BF02106733
published in: Siberian Mathematical Journal
publication date: 1997-11-06T00:00:00Z
review text: Let \(k\) be a field of characteristic not 2, \(k\neq\text{GF}(3)\), \(\text{GF}(9)\), and \(K\) an algebraic extension of \(k\). Let \(G\) be an irreducible subgroup of \(\text{GL}_n(K)\) (\(n\geq 2\)). The author proves that if \(G\) contains a root \(k\)-subgroup then, for some integers \(m\) and \(r\) with \(mr=n\), \(G\) contains a normal subgroup which is conjugate to the \(r\)th Cartesian product of a classical (special linear, special unitary, or symplectic) group of dimension \(m\) over a field between \(k\) and \(K\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 1023882
zbMATH Keywords: linear groups
zbMATH Keywords: subgroup lattices
zbMATH Keywords: root subgroups
zbMATH Keywords: normal subgroups
author: Evgenii L. Bashkirov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02106733
OpenAlex ID: W1998024490
description: scientific article; zbMATH DE number 1023882