The B-ovals of order \(q\leq 8\)
type: Item
instance of: scholarly article
title: The B-ovals of order \(q\leq 8\)
zbMATH Open document ID: 0532.51013
DOI: 10.1016/0097-3165(84)90038-4
author: Giorgio Faina
published in: Journal of Combinatorial Theory. Series A
publication date: 1984-01-01T00:00:00Z
review text: \textit{F. Buekenhout} introduced an abstract generalization of the concept of an oval in a projective plane in Rend. Mat. Appl., V. Ser. 25, 333-393 (1966; Zbl 0155.491). Such a B-oval consists of a set of \(q+1\) points together with a set of involutions acting (in an appropriate sense) sharply 2-transitively on these points; it is said to have order q, then. These structures are connected to certain partial geometries. In the present paper, all B-ovals of order at most 8 are classified. In particular, there are exactly 2 B-ovals (both of order 8) which do not come from an oval in a projective plane.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 3844514
zbMATH Keywords: Buekenhout ovals
zbMATH Keywords: projective oval
zbMATH Keywords: partial geometries
MaRDI profile type: Publication
full work available at URL: 0097-3165(84)90038-4
OpenAlex ID: W2003502654
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description: scientific article; zbMATH DE number 3844514