Flag-transitive subgroups of Chevalley groups with Abelian stabilizers
type: Item
instance of: scholarly article
title: Flag-transitive subgroups of Chevalley groups with Abelian stabilizers
zbMATH Open document ID: 0563.20040
DOI: 10.1007/BF02941482
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1985-01-01T00:00:00Z
review text: The groups named in the title are shown to leave a ''polarity'' of the associated Tits building invariant (under an additional technical hypothesis). This is used to prove the following theorem: Let G be a Chevalley group of rank \(\geq 2\) over the reals resp. over an algebraically closed field K. Then the flag-transitive subgroups of G with Abelian stabilizers are exactly the maximal compact subgroups of G resp. the groups \(\bar G(\)k) where k is a subfield of K with \([K:k]=2\), \(\bar G\) is a simple algebraic group defined over K with \(\bar G(\)K)\(=G\) and \(\bar G(\)k) is the group of points of \(\bar G\) over k for some k- compact k-structure on \(\bar G.\)
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 3897223
zbMATH Keywords: Tits building
zbMATH Keywords: Chevalley group
zbMATH Keywords: flag-transitive subgroups
zbMATH Keywords: abelian stabilizers
zbMATH Keywords: maximal compact subgroups
zbMATH Keywords: simple algebraic group
author: Helmut Völklein
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02941482
OpenAlex ID: W2063138232
description: scientific article; zbMATH DE number 3897223