Group theoretic characterizations of Buekenhout-Metz unitals in PG\((2,q^{2})\)
type: Item
instance of: scholarly article
title: Group theoretic characterizations of Buekenhout-Metz unitals in PG\((2,q^{2})\)
zbMATH Open document ID: 1229.51012
author: Giorgio Donati
author: Nicola Durante
published in: Journal of Algebraic Combinatorics
publication date: 2011-03-31T00:00:00Z
review text: Let \(G\) be the group of projectivities stabilizing a unital \(\mathcal{U}\) in PG\((2,q^{2})\) and let \(A,B\) be two distinct points of \(\mathcal{U}\). The authors prove that, if \(G\) has an elation group of order \(q\) with center \(A\) and a group of projectivities stabilizing both \(A\) and \(B\) of order greater than \(2(\sqrt{q}-1)\), then \(\mathcal{U}\) is an ovoidal Buekenhout-Metz unital. From this result two group theoretic characterizations of orthogonal Buekenhout-Metz unitals are given.
Mathematics Subject Classification ID: 51E99
Mathematics Subject Classification ID: 51A99
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 5872798
zbMATH Keywords: unitals
zbMATH Keywords: projectivities
zbMATH Keywords: elations
reviewed by: Basri Çelik
MaRDI profile type: Publication
full work available at URL: s10801-010-0250-8
OpenAlex ID: W2031938646
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DOI: 10.1007/S10801-010-0250-8
description: scientific article; zbMATH DE number 5872798