Unitals and inversive planes
type: Item
instance of: scholarly article
title: Unitals and inversive planes
zbMATH Open document ID: 0893.51008
DOI: 10.1007/BF01222925
author: Christine M. O'Keefe
author: S. G. Barwick
published in: Journal of Geometry
publication date: 1998-08-24T00:00:00Z
review text: Let \({\mathcal P}\) be a translation plane of dimension at most 2 over its kernel \(\text{GF} (q)\), and let \(U\) be a Buekenhout-Metz unital in \({\mathcal P}\). The authors show that \(U\) has an associated \(2-(q^2, q+1,q)\) design which is the point-residual of an inversive plane. This generalizes work by \textit{H. Wilbrink} [Lect. Notes Pure Appl. Math. 82, 445-454 (1983; Zbl 0507.05014)], \textit{R. Baker} and \textit{G. Ebert} [J. Comb. Theory, Ser. A 60, No. 1, 67-84 (1992; Zbl 0783.05031)], and \textit{G. Ebert} [Eur. J. Comb. 13, No. 2, 109-117 (1992; Zbl 0758.51006)]. The authors of this investigation use the geometry inherent in the Buekenhout-Metz unital construction, while Wilbrink' work is synthetic and the work of Baker and Ebert uses coordinates.
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 1000343
zbMATH Keywords: Buekenhout-Metz unital
zbMATH Keywords: point-residual
zbMATH Keywords: inversive plane
reviewed by: Michael J. Kallaher
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01222925
OpenAlex ID: W1988035586
description: scientific article; zbMATH DE number 1000343