Generalized quadrangles and regularity

Let S=(P,B,I) be a generalized quadrangle of order (s,t), s,t>1, and assume that S has a regular point X. In this paper we survey some basic results on such generalized quadrangles (GQs) as well as the known examples. We also study a general representation of such GQs using the net associated with the regular point X and specialise the representation to the case where X is abelian centre of symmetry, as in all of the known examples. © 2005 Elsevier B.V. All rights reserved