On some hyperbolic planes from finite projective planes

Basri Celik

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 25, 1-6

Abstract:

Let Π = ( P , L , I ) be a finite projective plane of order n , and let Π ′ = ( P ′ , L ′ , I ′ ) be a subplane of Π with order m which is not a Baer subplane (i.e., n ≥ m 2 + m ). Consider the substructure Π 0 = ( P 0 , L 0 , I 0 ) with P 0 = P \ { X ∈ P | X I l , l ∈ L ′ } , L 0 = L \ L ′ where I 0 stands for the restriction of I to P 0 × L 0 . It is shown that every Π 0 is a hyperbolic plane, in the sense of Graves, if n ≥ m 2 + m + 1 + m 2 + m + 2 . Also we give some combinatorial properties of the line classes in Π 0 hyperbolic planes, and some relations between its points and lines.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:568426

DOI: 10.1155/S0161171201006184

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