On a conjecture of R. H. Bruck
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.
scientific article; zbMATH DE number 3863212