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
On the structure of generalized quadrangles
โ Scribed by Clark T Benson
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 601 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We introduce the notion of subquadrangle regular system of a generalized quadrangle. A subquadrangle regular system of order m on a generalized quadrangle of order (s, t) is a set R of embedded subquadrangles with the property that every point lies on exactly m subquadrangles of R. If m is one half
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