Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 191-207 (2010)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Generalized quadrangles and projective axes of symmetry

Günter F. Steinke and Hendrik Van Maldeghem

Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand, e-mail:; Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium, e-mail:

Abstract: 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.

© 2010 Heldermann Verlag
© 2010–2013 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition