A geometric construction of generalized quadrangles from polar spaces of rank three
type: Item
instance of: scholarly article
title: A geometric construction of generalized quadrangles from polar spaces of rank three
zbMATH Open document ID: 0765.51006
DOI: 10.1007/BF03323091
published in: Results in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: This paper is devoted to the construction of generalized quadrangles from polar spaces of rank three. A generalized quadrangle is a thick polar space of rank two, that is an incidence structure such that: if a point \(x\) and a line \(L\) are not incident, then either all points of \(L\) are collinear with \(x\), or only one point of \(L\) is collinear with \(x\), furthermore, each line is incident with at least three points and each point is incident with at least three lines, and there is no point collinear with all the other points. The main result is a direct geometric construction of the generalized quadrangle from a polar space of rank three, that is a polar space whose maximal singular subspaces are projective planes. The results are interesting and, as the author points out, some generalized quadrangles, not associated with flocks, are obtained.
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 62174
zbMATH Keywords: generalized quadrangles
zbMATH Keywords: polar spaces of rank three
author: Norbert Knarr
reviewed by: Antonio Andreatta
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 62174