Two-transitive ovals in generalized twisted field planes
type: Item
instance of: scholarly article
title: Two-transitive ovals in generalized twisted field planes
zbMATH Open document ID: 1018.51008
author: Mauro Biliotti
author: Norman L. Johnson
author: Vikram Jha
published in: Archiv der Mathematik
publication date: 2002-12-01T00:00:00Z
review text: Let \(\pi\) be a finite affine plane whose projective extension contains an oval \(\Omega\) which intersects the line at infinity in a single point \((\infty)\), i.e. the line at infinity is tangent to \(\Omega\) at \((\infty) \). In this case \(\Omega\) is said to be a parabolic oval of \(\pi\). If there is a collineation group \(G\) of \(\pi\) which leaves \(\Omega\) invariant and acts 2-transitively on \(\Omega\setminus \{(\infty)\}\), we call \(\Omega\) a 2-transitive parabolic oval. The authors remark that, if \(\pi\) is a finite translation plane of odd order admitting a 2-transitive parabolic oval, then \(\pi\) is a commutative twisted field plane. Moreover, in [\textit{M. J. Ganley}, Geom. Dedicata 1, 103-116 (1972; Zbl 0241.50024)], it has been proved that commutative twisted field planes of odd order admit a 2-transitive parabolic oval. In this paper the authors prove that the only generalized twisted field plane of even order admitting a 2-transitive parabolic oval is the Desarguesian one.
reviewed by: Guglielmo Lunardon
Mathematics Subject Classification ID: 51E23
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 1837333
zbMATH Keywords: oval
zbMATH Keywords: translation plane
zbMATH Keywords: generalized twisted field plane
MaRDI profile type: Publication
full work available at URL: s00013-002-8309-y
OpenAlex ID: W2020383101
DOI: 10.1007/S00013-002-8309-Y
description: scientific article; zbMATH DE number 1837333