Some notes on generalized quadrangles of order \(s\) with a span of regular points
The authors prove that a finite generalized quadrangle of order \(q\) is a symplectic quadrangle, if it has a center \(x\) of symmetry such that the projective plane at \(x\) is desarguesian. The elementary proof uses admissible triples, as introduced in [\textit{B. De Bruyn}, Eur. J. Comb. 20, 759--771 (1999; Zbl 0946.51007)]. For stronger results see \textit{K. Thas} [Adv. Geom. 2, 189--196 (2002; Zbl 0998.51004)] and \textit{W. M. Kantor} [Adv. Geom. 2, 197--200 (2002; Zbl 0998.51003)].
scientific article; zbMATH DE number 5152737