Locally finite generalized quadrangles with at most five points per line

Finite Generalized Quadrangles

On Finite Elation Generalized Quadrangles with Symmetries

We study the structure of finite groups G which act as elation groups on finite generalized quadrangles and contain a full group of symmetries about some line through the base point. Such groups are related to the translation groups of translation transversal designs with parameters depending on those of the quadrangles. Using results on the structure of /^-groups which act as translation group...

Generalized quadrangles of order s with a hyperbolic line consisting of regular points

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).

The Classification of Generalized Quadrangles with Two Translation Points

Suppose S is a finite generalized quadrangle (GQ) of order (s, t), s 6= 1 6= t, and suppose that L is a line of S. A symmetry about L is an automorphism of the GQ which fixes every line of S meeting L (including L). A line is called an axis of symmetry if there is a full group of symmetries of size s about this line, and a point of a generalized quadrangle is a translation point if every line t...

Determination of generalized quadrangles with distinct elation points

In this paper, we classify the finite generalized quadrangles of order (s, t), s, t > 1, which have a line L of elation points, with the additional property that there is a line M not meeting L for which {L , M} is regular. This is a first fundamental step towards the classification of those generalized quadrangles having a line of elation points.