Hostname: page-component-7dd5485656-wlg5v Total loading time: 0 Render date: 2025-11-02T06:56:22.687Z Has data issue: false hasContentIssue false
  • English
  • Français

The Nonexistence of Certain Finite Projective Planes

Published online by Cambridge University Press:  20 November 2018

R. H. Bruck  and
H. J. Ryser
R. H. Bruck
Affiliation:
The University of Wisconsin
H. J. Ryser
Affiliation:
The University of Wisconsin
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A projective plane geometry π is a mathematical system composed of undefined elements called points and undefined sets of points (at least two in number) called lines, subject to the following three postulates:

(P1) Two distinct points are contained in a unique line.

(P2) Two distinct lines contain a unique common point.

(P3) Each line contains at least three points.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 1 , Issue 1 , 01 February 1949 , pp. 88 - 93
Copyright
Copyright © Canadian Mathematical Society 1949

References

[1] Bose, R. C., “On the application of the properties of Galois fields to the problem of construction of hyper-Graeco-Latin squares,” Sankhya, Indian Journal of Statistics, vol. 3 (1938), 323-338.Google Scholar
[2] Durfee, W. H., “Quadratic forms over fields with a valuation,” Bull. Amer. Math. Soc, vol. 54 (1948), 338–351.Google Scholar
[3] Hall, M., “Projective planes,” Trans. Amer. Math. Soc, vol. 54 (1943), 229-277.Google Scholar
[4] Hasse, H., “Über die Äquivalenz quadratischer Formen im Körper der rationalen Zahlen,” J.reine angew. Math., vol. 152 (1923), 205-224.Google Scholar
[5] Hilbert, D., Gesammelte Abhandlungen, I (Berlin, 1932), 161-173.Google Scholar
[6] F. W., Levi, Finite geometrical systems (University of Calcutta, 1942).Google Scholar
[7] MacDuffee, C. C., The theory of matrices (New York, 1946), 56.Google Scholar
[8] Mann, H. B., “On orthogonal Latin squares,” Bull. Amer. Math. Soc, vol. 50 (1944), 249–257.Google Scholar
[9] Minkowski, H., Gesammelte Abhandlungen, I (Leipzig and Berlin, 1911), 219-239.Google Scholar
[10] Pall, G., “The arithmetical invariants of quadratic forms,” Bull. Amer. Math. Soc, vol. 51 (1945), 185–197.Google Scholar
[11] Tarry, G., “Le problème de 36 officiers,” Compte Rendu de l'Association Française pour VAvancement de Science Naturel, vol. 1 (1900), 122-123, vol. 2 (1901), 170–203.Google Scholar
[12] Veblen, O. and Bussey, W. H., “Finite projective geometries,” Trans. Amer. Math.Soc, vol. 7 (1906), 241–259.Google Scholar
[13] Veblen, O. and Wedderburn, J. H. M., “Non-Desarguesian and non-Pascalian geometries,” Trans. Amer. Math. Soc, vol. 8 (1907), 379–388.Google Scholar
[14] MacNeish, H. F., “Euler squares,” Ann. of Math., vol. 23 (1921-22), 221–227.Google Scholar