Symmetry in generalized quadrangles (Q1404330)

In this paper some new points of view about Lenz(-Barlotti)-type classification of finite generalized quadrangles are described. Also, it is shown that each span-symmetric generalized quadrangle of order \(s>1\) with \(s\) even is isomorphic to \(Q(4,5)\) without using the canonical connection between groups of order \(s^3-s\) with a 4-gonal basis and span-symmetric generalized quadrangle of order \(s\). And, finally, a classification program for all finite translation generalized quadrangles is given.