Generalized Quadrangles with a Spread of Symmetry

Author: De Bruyn B.

Source: European Journal of Combinatorics, Volume 2, Number 8, November 1999 , pp. 759-771(13)

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Abstract:

We present a common construction for some known infinite classes of generalized quadrangles. Whether this construction yields other (unknown) generalized quadrangles is an open problem. The class of generalized quadrangles obtained this way is characterized in two different ways. On the one hand, they are exactly the generalized quadrangles having a spread of symmetry. On the other hand, they can be characterized in terms of the group of projectivities with respect to a spread. We explore some properties of these generalized quadrangles. All these results can be applied to the theory of the glued near hexagons, a class of near hexagons introduced by the author in De Bruyn (1998) On near hexagons and spreads of generalized quadrangles, preprint. Copyright 1999 Academic Press

Language: English

Document Type: Research article

Affiliations: Department of Pure Mathematics and Computer Algebra, University of Ghent, Galglaan 2, B-9000 Gent, Belgium

Publication date: 1999-11-01