Generalized quadrangles admitting PSL(2,q) × PSL(2,q)

In this paper, we classify the generalized quadrangles of order (s,t), s ≠ 1 ≠ t, which admit the natural action of PSL(2,s) × PSL(2,s) on a subGQ of order (s,1). This generalizes a recent result of J. De Kaey and H. Van Maldeghem 3 , by whom the classification was obtained for the case s = t. © 2005 Wiley Periodicals, Inc. J Combin Designs.