The doubly transitive flocks of quadratic cones
type: Item
instance of: scholarly article
title: The doubly transitive flocks of quadratic cones
zbMATH Open document ID: 0890.51006
published in: European Journal of Combinatorics
publication date: 1998-06-29T00:00:00Z
review text: In this paper, the authors classify all flocks of a quadratic cone in \(\text{PG} (3,q)\), \(q\) odd, admitting a doubly transitive automorphism group. In fact, by earlier results, it is enough to classify the doubly transitive semifield flocks. It turns out that only the Kantor flocks have that property. This follows from a more general classification of semifield flocks satisfying some strong divisibility condition (but satisfied in the doubly transitive case). Together with some earlier results of the authors [Geom. Dedicata 61, No. 1, 71-85 (1996; Zbl 0868.51013)], this gives the following theorem: A flock of an oval or quadratic cone in \(\text{PG} (3,q)\) admitting a doubly transitive automorphism group in \(\text{PGL}_4 (q)\) is either a translation oval flock of Thas \((q\) even), a Kantor flock \((q\) odd), a Fisher-Thas-Walker flock, or a linear flock (all \(q)\). The proof uses the associated spreads and translation planes.
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 1088573
zbMATH Keywords: flock of quadratic cone
zbMATH Keywords: semifield flocks
zbMATH Keywords: Kantor flocks
author: Vikram Jha
author: Norman L. Johnson
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
full work available at URL: eujc.1997.0157
OpenAlex ID: W2111873766
DOI: 10.1006/EUJC.1997.0157
description: scientific article; zbMATH DE number 1088573