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Characterizations of generalized quadrangles by generalized homologies

โœ Scribed by J.A Thas

Book ID
107885020
Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
646 KB
Volume
40
Category
Article
ISSN
0097-3165

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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 genera

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With any flock F of the quadratic cone K of PG(3, q) there corresponds a generalized quadrangle S(F) of order (q 2 , q). For q odd Knarr gave a pure geometrical construction of S(F) starting from F. Recently, Thas found a geometrical construction of S(F) which works for any q. Here we show how, for