During the final steps in the classification of the Moufang quadrangles by Jacques Tits and Richard Weiss a new class of Moufang quadrangles unexpectedly turned up. Subsequently Bernhard Mühlherr and Hendrik Van Maldeghem showed that this class arises as the fixed points and hyperlines of certain involutions of a metasymplectic space (or equivalently a building of type F4). In the same paper th...

In this paper, we establish the following two results: (1) a skew translation generalized quadrangle of even order is quadrangle, (2) does not admit point regular group automorphisms. The first result confirms conjecture Payne (1975) based on earlier work Ott (2021), and second Ghinelli (1992).

m *'* aiixr + ai2< + ■ ■ • + ai*+i°€li fi_, h, xk+i ak+nxi ~r an-i2a:2 + ■+ a*+i*+ia;i:+i where wi is zero or an integer less than n, is a collineation. As a result of Dr. Levi's article J it is possible to prove the converse proposition, namely, that every collineation in PG(k,pn) is of type (1). The following argument connects this theorem directly with our former article. It will be sufficie...

Payne [4] constructed an association scheme from a generalized quadrangle with a quasiregular point. We show that an association scheme with appropriate parameters and satisfying an assumption about maximal cliques must be one of these schemes arising from a generalized quadrangle.

We show that the generalized quadrangle W3(q) for odd q has exponentially many 12(q+1)–ovoids, thus implying that the generalized quadrangle Q(4, q) has exponentially many hemisystems for odd q. For q even, we show that W3(q) has m–ovoids for all integers m, 1 ≤ m ≤ q. Stabilizers are determined, and some computer results are given.

Mercury’s quadrangle H02 ‘Victoria’ is located in the planet’s northern hemisphere and lies between latitudes 22.5° N and 65° N, and between longitudes 270° E and 360° E. This quadrangle covers 6.5% of the planet’s surface with a total area of almost 5 million km. Our 1:3,000,000-scale geologic map of the quadrangle was produced by photo-interpretation of remotely sensed orbital images captured...

In an abelian category, a commutative quadrangle is called bicartesian if its diagonal sequence is short exact, i.e. if it is a pullback and a pushout. A commutative quadrangle is bicartesian if and only if we get induced isomophisms on the horizontal kernels and on the horizontal cokernels. In a triangulated category in the sense of Verdier [3, Def. 1-1], a commutative quadrangle is called hom...

A generalized quadrangle of order s ≥ 2 is isomorphic to W (s) if and only if there is a hyperbolic line every point of which is regular. This is a characterization of the symplectic generalized quadrangle W (s) which only needs the existence of s + 1 regular points (in a nice position).