Finite locally generalized quadrangles with affine planes

On the metric dimension of affine planes, biaffine planes and generalized quadrangles

In this paper the metric dimension of (the incidence graphs of) particular partial linear spaces is considered. We prove that the metric dimension of an affine plane of order q ≥ 13 is 3q − 4 and describe all resolving sets of that size if q ≥ 23. The metric dimension of a biaffine plane (also called a flag-type elliptic semiplane) of order q ≥ 4 is shown to fall between 2q−2 and 3q−6, while fo...

Finite Generalized Quadrangles

Locally polar geometries with affine planes

The study of geometries on the absolute points of polarities in projective spaces has been started by Veldkamp [21], who was the first to give a synthetic characterization of these geometries, which he called polar spaces. As part of his work on spherical buildings [19], Tits extended Veldkamp’s results to a somewhat larger class of geometries related to pseudo-quadratic forms. In 1974, Buekenh...

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...

Spreads and ovoids of finite generalized quadrangles

We survey recent results on spreads and ovoids of finite generalized quadrangles. Included in the survey are results on ovoids of PG(3, q); translation ovoids of Q(4, q); characterisations of generalized quadrangles using subquadrangles and ovoids of subquadrangles; and spreads of T2(Ω).