An identification theorem for the locally finite nontwisted Chevalley groups
type: Item
instance of: scholarly article
title: An identification theorem for the locally finite nontwisted Chevalley groups
zbMATH Open document ID: 0535.20016
DOI: 10.1007/BF01192748
author: Simon Thomas
published in: Archiv der Mathematik
publication date: 1983-01-01T00:00:00Z
review text: In this paper, a Chevalley group means a nontwisted Chevalley group. The main result of this paper is: Theorem. Let \(G=\cup_{i\in \omega}G_ i\) where each \(G_ i\) is isomorphic to a Chevalley group of type \({\mathcal L}\) over a finite field. Then G is isomorphic to a Chevalley group of type \({\mathcal L}\) over a locally finite field. Let \(\Phi\) denote a root system for Chevalley groups of type \({\mathcal L}\). The proof of this result uses: a result of Bryant to construct root subgroups \(X_ r\) for each \(r\in \Phi\), a result of Kegel to identify the subgroups \(<X_ r,X_{-r}>\) for each \(r\in \Phi\) and a theorem of Steinberg to identify G.
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E32
zbMATH DE Number: 3849479
zbMATH Keywords: locally finite field
zbMATH Keywords: root system
zbMATH Keywords: Chevalley groups
zbMATH Keywords: root subgroups
reviewed by: Morton E. Harris
MaRDI profile type: Publication
cites work: Groups with the minimal condition on centralizers
cites work: Q5662096
cites work: Über einfache, lokal endliche Gruppen
cites work: Q5675882
cites work: Q5549108
full work available at URL: https://doi.org/10.1007/bf01192748
OpenAlex ID: W2084899236
description: scientific article; zbMATH DE number 3849479