Groups contained between groups of Lie type over various fields
type: Item
instance of: scholarly article
title: Groups contained between groups of Lie type over various fields
zbMATH Open document ID: 0544.20040
DOI: 10.1007/BF01982115
author: Ya. N. Nuzhin
published in: Algebra and Logic
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187239
review text: Let \(G(R)\) be a Chevalley group over a field \(R\) and let \(K/R\) be an algebraic field extension. The author considers groups \(M\) such that \(G(R)\subset M\subset G(K)\). For more details assume that \(| R|>1+\max(r,r)/(s,s)\) where \(r,s\) are simple roots, as well as the rank of \(G\) is \(>1\) (a misprint: it is typed \(G>1\)). Assume also that \(R\) is perfect if \(1<char R<\max(r,r)/(s,s)\). Theorem 1 asserts that \(G(R)\subset M\subset G(K)\) implies \(G(P)\subset M\subset\widehat G(P)\) under these assumptions where \(P\) is a field and \(R\subset P\subset K\) and \(\widehat G(P)\) is an extended Chevalley group, that is the group \(G(R)\) extended by diagonal automorphisms. Actually Theorem 1 is valid under the weaker assumption \(M\cap x_ r(R)\neq 0\) for any root \(r\) instead of \(M\supset G(R)\). Moreover the author proves a certain version of this theorem for twisted forms of Chevalley groups.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 3865578
zbMATH Keywords: twisted Chevalley groups
zbMATH Keywords: simple roots
zbMATH Keywords: diagonal automorphisms
Wikidata QID: Q115393014
MaRDI profile type: Publication
cites work: Q3950737
cites work: Q3890894
cites work: Generating sets of root elements of Chevalley groups over a field
cites work: Q5662096
cites work: Q4123529
description: scientific article; zbMATH DE number 3865578