Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transi\-tive generalized quadrangles
type: Item
instance of: scholarly article
title: Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transi\-tive generalized quadrangles
zbMATH Open document ID: 1078.51004
author: Koen Thas
author: Hendrik Van Maldeghem
published in: Discrete Mathematics
publication date: 2005-06-23T00:00:00Z
review text: The authors give a very readable description of the history of generalized quadrangles which satisfy the Moufang condition, or some weaker condition, up to 2003. Moreover, they classify all finite thick generalized quadrangles which are quasi-transitive (this is a natural transitivity condition for generalized homologies). As a consequence they obtain the following result (without using the classification of finite simple groups): A finite thick generalized quadrangle is classical or dual classical if and only if it admits a BN-pair and a non-trivial homology.
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 05E20
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 20E42
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 2182141
zbMATH Keywords: generalized quadrangle
zbMATH Keywords: Moufang condition
zbMATH Keywords: BN-pair
MaRDI profile type: Publication
full work available at URL: j.disc.2004.04.047
OpenAlex ID: W2039488771
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DOI: 10.1016/J.DISC.2004.04.047
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description: scientific article; zbMATH DE number 2182141