Affine Generalized Quadrangles – An Axiomatization |
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Authors: | Harm Pralle |
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Institution: | 1. Mathematisches Institut der Justus-Liebig-Universit?t Giessen, Arndtstr. 2, D-35392, Giessen, Germany
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Abstract: | The complement of a geometric hyperplane of a generalized quadrangle is called an affine generalized quadrangle. Since a geometric hyperplane of a generalized quadrangle is either an ovoid or the perp of a point or a subquadrangle, there are three quite different classes of affine generalized quadrangles. The article proposes seven axioms (AQ1)–(AQ7) characterizing affine generalized quadrangles as point-line geometries. Certain subsets of the seven Axioms together with certain conditions distinguish what kind of hyperplane complement is realized. By just (AQ1)–(AQ6), finite affine generalized quadrangles are characterized completely. |
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