On a conjecture of R. H. Bruck
type: Item
instance of: scholarly article
title: On a conjecture of R. H. Bruck
zbMATH Open document ID: 0543.05015
DOI: 10.1016/0097-3165(84)90016-5
author: N. E. Zubov
published in: Journal of Combinatorial Theory. Series A
publication date: 1984-01-01T00:00:00Z
review text: The authors study a conjecture of R. H. Bruck. \textit{R. H. Bruck} [C. I. M. E., II. Ciclo Bressanone 1972, Finite Geom. Struct. Appl., 105-188 (1973; Zbl 0264.05013)] conjectured that for a prime power p, the 3- dimensional projective geometry PG(3,q) of points and lines might be extended to a projective plane of order \(q(q+1)\) by adding more points and lines but retaining the point-line incidences of PG(3,q). In this paper this conjecture is investigated in a search for a possible plane of order 12 arising from the projective geometry PG(3,3). A complete search shows that this extension is impossible.
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 3863212
zbMATH Keywords: projective geometry
zbMATH Keywords: projective plane
Wikidata QID: Q123357286
reviewed by: Mario Gionfriddo
MaRDI profile type: Publication
full work available at URL: 0097-3165(84)90016-5
OpenAlex ID: W2059147451
cites work: Circle geometry in higher dimensions. II
cites work: Codes and designs
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description: scientific article; zbMATH DE number 3863212