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Generalized Quadrangles with a Spread of Symmetry

โœ Scribed by Bart De Bruyn

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
173 KB
Volume
20
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

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A sufficient condition for the simple connectedness is given for an infinite family of extended generalized quadrangles Y(S) of order (q + 1, q -1) constructed in [7] from a family S of planes in PG(5, q) with some conditions. Applying this, Y(S) is shown to be simply connected when S is obtained fr

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In this paper we show that any dual of the family S of planes defined by Yoshiara [6] also satisfies the same conditions. We present a new family Y (O) of extended generalized quadrangles of order (q + 1, q -1) constructed from the dual of the Yoshiara construction S(O) [6] and show that each such e