On near hexagons and spreads of generalized quadrangles
type: Item
instance of: scholarly article
title: On near hexagons and spreads of generalized quadrangles
zbMATH Open document ID: 0961.51004
DOI: 10.1023/A:1008709716107
author: Bart De Bruyn
published in: Journal of Algebraic Combinatorics
publication date: 2001-05-11T00:00:00Z
review text: A generalized quadrangle is a connected partial linear space for which the diameter of the point graph \(\Gamma\) is two and such that for every point \(p\) and every line \(L\), there is a unique point \(q\) on \(L\) nearest to \(p\). And similarly, a near hexagon is a connected partial linear space for which the diameter of the point graph \(\Gamma\) is three and such that for every point \(p\) and every line \(L\), there is a unique point \(q\) on \(L\) nearest to \(p\). A spread of a generalized quadrangle is a set of lines which partitions the point set of the generalized quadrangle. The above mentioned incidence structures can be linked to each other since generalized quadrangles can appear as geodetically closed subsets within near hexagons. The author makes use of this relation between generalized quadrangles and near hexagons by presenting a glueing-construction, making use of two generalized quadrangles with a spread in each of them, which yields under some conditions a near hexagon. These latter hexagons are called glued near hexagons. This construction is applied to different generalized quadrangles having a spread, leading to new examples of near hexagons. Also the properties of these glued near hexagons are investigated. This information on the properties is then used to characterize the glued near hexagons within the set of all near hexagons.
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 51E23
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 1495745
zbMATH Keywords: near hexagons
zbMATH Keywords: generalized quadrangles
zbMATH Keywords: spreads
reviewed by: Leo Storme
MaRDI profile type: Publication
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full work available at URL: a:1008709716107
OpenAlex ID: W1482002023
description: scientific article; zbMATH DE number 1495745