A characterization of Buekenhout-Metz unitals in PG\((2,q^ 2)\), \(q\) even
type: Item
instance of: scholarly article
title: A characterization of Buekenhout-Metz unitals in PG\((2,q^ 2)\), \(q\) even
zbMATH Open document ID: 0843.51013
DOI: 10.1007/BF00155725
published in: Geometriae Dedicata
publication date: 1996-08-18T00:00:00Z
review text: A unital (Hermitian arc) \(U\) in \(PG(2,q^2)\) is a set of \(q^3 + 1\) points such that the intersections of lines with \(U\) either consists of a single point or \(q + 1\) points. The absolute points and non-absolute lines of a non-degenerate unitary polarity form a ``classical unital''. The authors use the term ``\(B\)-unital'' to denote any unital constructed from an ovoid in \(PG(3,q)\) by a method of Buekenhout. If the ovoid is an elliptic quadric, they call it a \(B\)-\(M\) unital. [Note: In another paper reviewed in this same edition of Zbl, the authors use the term ``\(B\)-\(M\) unital'' with the same meaning as ``\(B\)-unital'' in the present paper.] The main result of the present paper is that if \(q\) is a power of 2, a \(B\)-unital \(U\) in \(PG(2,q^2)\) is a \(B\)-\(M\) unital if there is a point \(A\) on \(U\) such that the stabilizer of \(A\) in the linear collineation group fixing \(U\) has a subgroup which is sharply transitive on \(U\)-\(A\).
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 843608
zbMATH Keywords: Buekenhout-Metz unitals
author: Vito Abatangelo
author: Bambina Larato
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00155725
OpenAlex ID: W1997504833
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description: scientific article; zbMATH DE number 843608