Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 51, No. 1, pp. 191207 (2010) 

Generalized quadrangles and projective axes of symmetryGünter F. Steinke and Hendrik Van MaldeghemDepartment of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand, email: G.Steinke@math.canterbury.ac.nz; Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B9000 Gent, Belgium, email: hvm@cage.UGent.beAbstract: We investigate generalized quadrangles $\Gamma$ that admit at least two projective axes of symmetry. We show that if there are three such axes incident with a common point $x$, then $x$ is a translation point of $\Gamma$. In case that $\Gamma$ is moreover a compact connected quadrangle with topological parameters $(p,p)$, $p\in\N$, then $\Gamma$ is a topological translation generalized quadrangle. We further investigate the case of two opposite projective axes of symmetry and obtain a characterization of the dual of the symplectic quadrangle over $\R$ or $\C$ among compact connected quadrangles with equal topological parameters. Full text of the article:
Electronic version published on: 27 Jan 2010. This page was last modified: 28 Jan 2013.
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