A remark on presentations of certain Chevalley groups.
type: Item
instance of: scholarly article
title: A remark on presentations of certain Chevalley groups.
zbMATH Open document ID: 1041.20032
DOI: 10.1007/BF02638375
published in: Archiv der Mathematik
publication date: 2003-03-27T00:00:00Z
review text: Let \(\Phi\) be a root system of type \(A_l\), \(l\geq2\); \(D_l\), \(l\geq4\); or \(E_l\), \(6\leq l\leq8\). Let \(G\) be a group generated by nonidentity Abelian subgroups \(A_r\), \(r\in\Phi\), and subject to certain relations that are slightly more general than those given by \textit{F. G. Timmesfeld} [Geom. Dedicata 73, No. 1, 85-117 (1998; Zbl 0919.20021)]. The author shows that \(\Phi\) is the disjoint union of irreducible root subsystems \(\Psi_i\) of \(\Phi\) with certain conditions. As a consequence, \(G\) is a central product of groups \(G_i\) which are related to the \(\Psi_i\).
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 1889268
zbMATH Keywords: Chevalley groups
zbMATH Keywords: root systems
zbMATH Keywords: presentations
author: F. G. Timmesfeld
MaRDI profile type: Publication
cites work: Q5662096
cites work: Q2731785
cites work: Presentations for certain Chevalley groups
full work available at URL: https://doi.org/10.1007/bf02638375
OpenAlex ID: W2003589847
description: scientific article; zbMATH DE number 1889268