A Connection Between Projective Planes and Generalized Quadrangles |
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15 lines 15 points 3-regular absolute line absolute points antiregular axiom CALIFORNIA/SANTA CRUZ Ty CALIFORNIA/SANTA CRUZ UNIVERSITY classical GQ's collinear complete oval contradiction count in different CRUZ Th CRUZ The University d₁ d₂ define definition denote diagonals of Q distinct points Dixmier and Zara Dually eigenvalue elements exterior line Fano Plane finite projective plane geometries GQ of order hyperbolic line hyperoval incidence graph incidence structure integer intersect isomorphic Jacques Tits least one absolute Library The University line contains m₁ m₂ non-collinear points number of absolute number of ordered number of points one-to-one correspondence Payne plane of order polarity projective space Proof proposition 6.2.2 prove the uniqueness quadrangle of order real line SANTA CRUZ UNIVERSITY secant lines self-dual spread subspace Suppose synthemes tangent line Thas Theorem Tits unique line unique ovoid University Library UNIVERSITY UNIVERSITY OF CALIFORNIA UNIVERSITY OF CALIFORNIA/SANTA VERSITY OF CALIFORNIA/SANTA