## A Connection Between Projective Planes and Generalized Quadrangles |

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### Contents

Generalized Quadrangles | 15 |

Classification of Known Generalized Quadrangles | 19 |

Generalized Quadrangles of Small Parameter | 24 |

2 other sections not shown

### Common terms and phrases

15 lines 15 points 3-regular absolute line absolute points antiregular axiom classical generalized quadrangles classical GQ's collinear is called complete oval construction of GQ(2 contradiction count in different define definition denote diagonals of Q distinct lines distinct points Dixmier and Zara Dually eigenvalue elements exists exterior line Fano Plane Finite Geometries finite projective plane geometries GQ of order hyperbolic line hyperoval incidence graph incidence structure integer intersect isomorphic Jacques Tits least one absolute lemma line contains lines of P,L meet H non-absolute lines non-collinear points number of absolute number of ordered number of points one-to-one correspondence plane of order point is regular points of H polygons prime power projective space Proof proposition 6.2.2 prove the uniqueness quadrangle of order quadric real line secant line self-dual simple eigen root subspace Suppose symmetric relation synthemes tangent line Theorem Tits unique line unique ovoid unique point incident