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Generalized quadrangles of order 4. I

✍ Scribed by Stanley E Payne

Publisher: Elsevier Science
Year: 1977
Tongue: English
Weight: 693 KB
Volume: 22
Category: Article
ISSN: 0097-3165
DOI: 10.1016/0097-3165(77)90002-4

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✍ Stanley E Payne 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 436 KB

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✍ J.A. Thas 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 212 KB

Let S=(P, B, I) be a generalized quadrangle of order (q, q 2 ), q>1, and assume that S satisfies Property (G) at the flag (x, L). If q is odd then S is the dual of a flock generalized quadrangle. This solves (a stronger version of ) a ten-year-old conjecture. We emphasize that this is a powerful the

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✍ J.A Thas 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 514 KB

ac.be. \* . The set of all points r i \* is denoted by B; we have |B| =q 2n . Further, let A be the set of all intersections of PG(n+1, q n ) with the tangent lines of the conics C i at s 1 . The tangent line U i of C i at s 1 belongs to {Ä , hence of B and just one point of A. Let ? be the plane c

All generalized quadrangles of order 3 a

All generalized quadrangles of order 3 are known

✍ Stanley E Payne 📂 Article 📅 1975 🏛 Elsevier Science 🌐 English ⚖ 203 KB

3-regularity in generalized quadrangles

3-regularity in generalized quadrangles of order (s, s2)

✍ J. A. Thas 📂 Article 📅 1984 🏛 Springer 🌐 English ⚖ 194 KB

If (x,y,z) is a 3-regular triad of a generalized quadrangle S=(P,B,I) of order (s, s2), s even, then {x,y,z}lu {x, y,z} ±± is contained in a subquadrangle of order s. As an application it is proved that a generalized quadrangle of order (4, 16) with at least one 3-regular triad is isomorphic to the

Generalized Hexagons as Amalgamations of

Generalized Hexagons as Amalgamations of Generalized Quadrangles

✍ H. Van Maldeghem; I. Bloemen 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 478 KB

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