Irregular hyperovals in \(PG(2,64)\)
type: Item
instance of: scholarly article
title: Irregular hyperovals in \(PG(2,64)\)
zbMATH Open document ID: 0821.51007
DOI: 10.1007/BF01226860
author: Tim Penttila
author: Ivano Pinneri
published in: Journal of Geometry
publication date: 1994-12-08T00:00:00Z
review text: For many years an open question was if any hyperoval of \(PG(2,64)\) is regular (that is a non-degenerate conic plus his nucleus). In this article two irregular hyperovals in \(PG(2,64)\) of order 64 are constructed. One has a collineation stabiliser of order 60, the other has a stabiliser of order 15. It is also shown, with the aid of a computer, that there are no more irregular hyperovals of \(PG(2,64)\) stabilised by a collineation of order 5.
reviewed by: Giustina Pica
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 700401
zbMATH Keywords: \(k\)-arcs
zbMATH Keywords: protective semilinear group
zbMATH Keywords: collineation stabiliser
zbMATH Keywords: irregular hyperovals of \(PG(2,64)\)
MaRDI profile type: Publication
Wikidata QID: Q29035985
cites work: Q5796828
cites work: On the connection between the ordinary and the modular characters of groups of finite order
cites work: Q3796299
cites work: Q5685093
cites work: Ovals in the Desarguesian plane of order 16
cites work: Ovals in Desarguesian planes of even order
cites work: Q3851217
cites work: Endliche Gruppen I
cites work: Q3205884
cites work: Q3276279
cites work: Q3988080
cites work: Q3769506
cites work: Q5815962
cites work: Ovals In a Finite Projective Plane
cites work: Q3260067
cites work: Q3843291
cites work: Ovali ed altre curve nei piani di Galois di caratteristica due
cites work: Q3288588
cites work: A family of ovals with few collineations
description: scientific article; zbMATH DE number 700401