Groups of projectivities of generalized quadrangles
type: Item
instance of: scholarly article
title: Groups of projectivities of generalized quadrangles
zbMATH Open document ID: 0926.51008
DOI: 10.1023/A:1005068106765
author: Leen Brouns
author: Katrin Tent
author: Hendrik Van Maldeghem
published in: Geometriae Dedicata
publication date: 1999-11-21T00:00:00Z
review text: For some reason the study of groups of projectivities of generalized quadrangles did not yet receive the attention due, although the study of groups of projectivities of projective planes produced a number of remarkable classification results. This paper rights this wrong. Characterizations of some classical generalized quadrangles with regular points or lines by properties of the group of projectivities are given. In particular, all finite classical generalized quadrangles with regular lines and all symplectic quadrangles over quadratically closed fields are characterized. The proof of the results employs the coordinatization of generalized quadrangles introduced by \textit{G. Hanssens} and \textit{H. Van Maldeghem} [Ann. Discrete Math. 37, 195-207 (1988; Zbl 0643.51011)].
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 1240980
zbMATH Keywords: perspectivities
zbMATH Keywords: projectivities
zbMATH Keywords: generalized polygon
zbMATH Keywords: von Staudt
zbMATH Keywords: Moufang quadrangle
reviewed by: Andreas E. Schroth
MaRDI profile type: Publication
full work available at URL: a:1005068106765
OpenAlex ID: W1403320
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description: scientific article; zbMATH DE number 1240980