Unitals which meet Baer subplanes in 1 modulo \(q\) points
type: Item
instance of: scholarly article
title: Unitals which meet Baer subplanes in 1 modulo \(q\) points
zbMATH Open document ID: 0959.51010
DOI: 10.1007/BF01221057
author: Christine M. O'Keefe
author: S. G. Barwick
author: Leo Storme
published in: Journal of Geometry
publication date: 2001-04-24T00:00:00Z
review text: Let \(\pi\) be a translation plane of order \(q^2\) with kernel containing \(GF(q)\). A unital in \(\pi\) is a set \(\mathcal U\) of \(q^3+1\) points such that each line meets \(\mathcal U\) in either \(1\) or \(q+1\) points. A unital in \(\pi\) is called parabolic if the translation line of \(\pi\) is a tangent of \(\mathcal U\). The authors prove that a parabolic unital \(\mathcal U\) in \(\pi\) is a Buekenhout-Metz unital (a parabolic unital arising by a construction due to Buekenhout) if and only if suitable Baer subplanes containing the translation line of \(\pi\) meet \(\mathcal U\) in \(1\) modulo \(q\) points. As a by-product, they show that a unital \(\mathcal U\) in \(PG(2,q^2)\) is classical (a Hermitian curve) if and only if it meets each Baer subplane of \(PG(2,q^2)\) in \(1\) modulo \(q\) points.
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 1507991
zbMATH Keywords: translation planes
zbMATH Keywords: parabolic unital
zbMATH Keywords: Buekenhout-Metz unital
zbMATH Keywords: Baer subplane
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1507991