Irreducible collineation groups fixing a hyperoval
type: Item
instance of: scholarly article
title: Irreducible collineation groups fixing a hyperoval
zbMATH Open document ID: 1018.51007
DOI: 10.1016/S0021-8693(02)00058-3
published in: Journal of Algebra
publication date: 2002-11-28T00:00:00Z
review text: An automorphism group \(G\) of a finite projective plane \(\pi\) is called irreducible if \(G\) fixes no point, line or triangle of \(\pi\). The authors investigate the case that \(G\) fixes a hyperoval and that the order \(n\) of \(\pi\), which is necessarily even, is divisible by 4. The only known examples seem to be a conic plus its nucleus in \(PG(2,4)\) and the Lunelli-Sce-Hall hyperoval in \(PG(2,16)\). It turns out that the general situation closely resembles these two cases. If \(G\) contains involutory elations and \(n \not= 4\) then the group generated by all involutory elations modulo its center is isomorphic to its counterpart associated with the Lunelli-Sce-Hall hyperoval, i.e. it is a generalized Hessian group of order 18. This result indicates that the Lunelli-Sce-Hall hyperoval might be only the first representative of an infinite family of hyperovals and that this family can be constructed by an inductive process.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1836716
zbMATH Keywords: Lunelli-Sce-Hall hyperoval
zbMATH Keywords: irreducible collineation groups
Wikidata QID: Q59249243
author: A. Bonisoli
author: Gabor Korchmáros
MaRDI profile type: Publication
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full work available at URL: s0021-8693(02)00058-3
OpenAlex ID: W2085914150
description: scientific article; zbMATH DE number 1836716