On finite generalized quadrangles of even order

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...

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).

Automorphisms and characterizations of finite generalized quadrangles

Our paper surveys some new developments in the theory of automorphisms and characterizations of finite generalized quadrangles. It is the purpose to mention important new results which did not appear in the following standard works (or surveys) on the subject: Collineations of finite generalized quadrangles (S. E. Payne, 1983), Finite Generalized Quadrangles (S. E. Payne and J. A. Thas, 1984), ...

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-...