On the universal embedding of the near-hexagon for \(U_ 4(3)\)
type: Item
instance of: scholarly article
title: On the universal embedding of the near-hexagon for \(U_ 4(3)\)
zbMATH Open document ID: 0843.51007
DOI: 10.1007/BF01263610
author: Matthew Kirby Bardoe
published in: Geometriae Dedicata
publication date: 1995-10-17T00:00:00Z
review text: The author determines the dimension of a vector space \(V\) over \({\mathcal F}_2\) such that there is a (universal) embedding of near-hexagon geometry \(\Gamma\) for \(U_4(3)\) in \(V\). Thus the geometry \(\Gamma\) is defined as a structure with 6-frames as points and 2-frames as lines in a vector space \({\mathcal F}^6_3\) equipped with the form \(q\) defined by \(q(x) = \sum^6_{i = 1} x^2_i\). Author (re-)proves that \(\dim V \leq 21\) using quite elementary techniques of linear algebra and studying in more details suborbits of the geometry \(\Gamma\) and connected components of points in each suborbit.
reviewed by: K. Prażmowski
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 806242
zbMATH Keywords: near-hexagon
zbMATH Keywords: embedding
zbMATH Keywords: suborbit diagram
zbMATH Keywords: connected component
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01263610
OpenAlex ID: W2025368653
description: scientific article; zbMATH DE number 806242