On the geometry of Baer subplanes in \(PG(2,4)\)
type: Item
instance of: scholarly article
title: On the geometry of Baer subplanes in \(PG(2,4)\)
zbMATH Open document ID: 0977.51003
author: Harald Gottschalk
published in: European Journal of Combinatorics
publication date: 2002-01-21T00:00:00Z
review text: The author recalls basic facts on hyperovals, Baer subplanes of \(PG(2,4)\), unitals and the Gewirtz graph. Then he defines certain sets of Baer subplanes in \(PG(2,4)\) called butterflies. These butterflies are used to determine parameters of the graph \(\Gamma\) on \(\mathbb{C}\) which is an \(L_3(4)\)-orbit of Baer subplanes in \(PG(2,4)\). It is shown that \(\Gamma\) is the collinearity graph of the geometry (101) of Buekenhout with the diagram \[ \underset {1}\circ\diagrtripleBar\underset {2}\circ\overset{\vtop{=2em\centerline{1079}\vglue 5pt}}\diagrtriplebar\underset {1}\circ. \] Moreover, the author proves that, if \(L_3(4)\) or \(L_3(4):2_1\) are automorphism groups, this geometry is determined up to isomorphism by its diagram.
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 1538572
zbMATH Keywords: Buekenhout diagram
zbMATH Keywords: hyperovals
zbMATH Keywords: unitals
zbMATH Keywords: Gewirtz graph
zbMATH Keywords: Baer subplanes of \(PG(2,4)\)
reviewed by: Pavel Burda
MaRDI profile type: Publication
full work available at URL: eujc.1999.0391
OpenAlex ID: W2058732455
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DOI: 10.1006/EUJC.1999.0391
description: scientific article; zbMATH DE number 1538572