A characterization of the finite Moufang hexagons by generalized homologies

A Characterization of the Finite Moufang Hexagons by Generalized Homologies

A generalized homology of a generalized hexagon 5^ is an auto-morphism of S? fixing all points on two mutually opposite lines or fixing all lines through two mutually opposite points. We show that if 5? is finite and if it admits "many" generalized homologies, then 5? is Moufang and hence classical. 1. Introduction and notation, A (finite thick) generalized hexagon of order (s, t) is a point-li...

The Finite Moufang Hexagons Coordinatized

We introduce coordinates for the nite Moufang hexagons and show with a few applications that this approach makes these objects less mysterious.

Characterizations of Generalized Quadrangles by Generalized Homologies

Let S= (P, B, I) be a generalized quadrangle of order (s, t). For X, y E P, X+ y. let X(x, y) be the group of all collineations of S fixing x and y linewise. If ZE (4 YJL> then the set of all points incident with the line xz (resp. y;) is denoted by z(resp. 3. The generalized quadrangle S = (P, B, I) is said to be (x, y)-transitive, x+ y, if X(x, y) is transitive on each set Z{x, z} and jZ’-{ y...

Ovoids and Spreads of Finite Classical Generalized Hexagons and Applications

Embedded Thick Finite Generalized Hexagons in Projective Space

We show that every embedded finite thick generalized hexagon J£" of order (s, t) in PG(n, q) which satisfies the conditions (0 s = q, (ii) the set of all points of J f generates PG(n, q), (iii) for any point x of Jf, the set of all points collinear in Jtf with x is contained in a plane of PG(n,q), (iv) for any point x of Jif, the set of all points of J f not opposite x in J f is contained in a ...