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Generalized Hexagons as Amalgamations of Generalized Quadrangles

โœ Scribed by H. Van Maldeghem; I. Bloemen

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
478 KB
Volume
14
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

We define the notion of regular point (p) in a generalized hexagon and show how a derived geometry at such a point can be defined. We motivate this by proving that, for finite generalized hexagons of order ((s, t)), this derivation is a generalized quadrangle iff (s=t). Moreover, if the generalized hexagon has also a regular line incident with (p), then one can amalgamate the two corresponding generalized quadrangles and in this way reconstruct the generalized hexagon. The small Moufang hexagons of order (3^{h}), for small (h), are characterized in this manner.

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