Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles

Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles

We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...

Finite Generalized Quadrangles

Generalized Quadrangles and Transitive Pseudo-Hyperovals

A pseudo-hyperoval of a projective space PG(3n− 1, q), q even, is a set of q +2 subspaces of dimension n − 1 such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabiliser is elementary. We then deduce from this result a classification of the thick generalised quadrangles Q that admit a point-primitive, line-transitive automorphism group wit...

Local Sharply Transitive Actions on Finite Generalized Quadrangles

We classify the finite generalized quadrangles containing a line L such that some group of collineations acts sharply transitively on the ordered pentagons which start with two points of L. This can be seen as a generalization of a result of Thas and the second author [22] classifying all finite generalized quadrangles admitting a collineation group that acts transitively on all ordered pentago...

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).