The Non-Existence of Finite Projective Planes of Order 10

Lam, C. W. H. ; Thiel, L. ; Swiercz, S.

Canadian journal of mathematics, Tome 41 (1989) no. 6, pp. 1117-1123

Résumé

A finite projective plane of order n,with n > 0, is a collection of n 2+ n + 1 lines and n2 + n + 1 points such that1. every line contains n + 1 points,2. every point is on n + 1 lines,3. any two distinct lines intersect at exactly one point, and4. any two distinct points lie on exactly one line.It is known that a plane of order n exists if n is a prime power. The first value of n which is not a prime power is 6. Tarry [18] proved in 1900 that a pair of orthogonal latin squares of order 6 does not exist, which by Bose's 1938 result [3] implies that a projective plane of order 6 does not exist.

Détail

DOI : 10.4153/CJM-1989-049-4

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