Chamber systems, geometries and parabolic systems whose diagram contains only bonds of strength 1 and 2
type: Item
instance of: scholarly article
title: Chamber systems, geometries and parabolic systems whose diagram contains only bonds of strength 1 and 2
zbMATH Open document ID: 0709.51015
DOI: 10.1007/BF01233427
published in: Inventiones Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143834
review text: This paper contributes to the classification of locally finite transitive chamber systems of rank \(\geq 3\). It namely pins down the possibilities for such chamber systems in characteristic 2 assuming the diagram contains at least one bond of strength 2 (i.e. the star of at least one cell of cotype 2 is the chamber system of a generalized quadrangle), but none of strength \(>2\) and moreover, no star of type \(C_ 3\) or \(A_ 3\) (``polar'' or projective 3-space) has the alternating group Alt(7) as induced automorphism group. A similar result is known for geometries containing a star (or residue) related to Alt(7), so this finishes the characteristic 2 case with still the other restrictions above. (The case of characteristic \(>3\) is handled by \textit{F. G. Timmesfeld}, Invent. Math. 87, 603-641 (1987; Zbl 0607.20019)].)
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 51B25
Mathematics Subject Classification ID: 20E42
zbMATH DE Number: 4165882
zbMATH Keywords: Buekenhout-Tits geometries
zbMATH Keywords: building-like geometries
zbMATH Keywords: classification
zbMATH Keywords: chamber systems
author: Gernot Stroth
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
cites work: Tits geometries over gf(2) Defined by groups over gf(3)
cites work: An enemies list for factorization theorems
cites work: Extensions of the chamber system of type \(A_ 3\) for \(A_ 7\)
cites work: Some geometries that are almost buildings
cites work: Some exceptional 2-adic buildings
cites work: On quadratic GF(2)-modules for Chevalley groups over fields of odd order
cites work: Q3324546
cites work: Q3934592
cites work: Sheaves on buildings and modular representations of Chevalley groups
cites work: Minimal parabolic geometries for the sporadic groups
cites work: Some sporadic geometries having \(C_ 3\)-residues of type \(A_ 7\)
cites work: One node extensions of buildings
cites work: Geometries of type M related to \(A_ 7\)
cites work: The nonexistence of certain Tits geometries with affine diagram
cites work: Minimal parabolic systems and small representations
cites work: Tits geometries and parabolic systems in finitely generated groups. I
cites work: Classical locally finite Tits chamber systems of rank 3
cites work: Locally finite classical Tits chamber systems of large order
cites work: Q3694160
description: scientific article; zbMATH DE number 4165882