Note on span-symmetric generalized quadrangles (Q2783475)

Let \(\mathcal L\) be a generalized quadrangle of order \((s, t)\), \(s, t >1\). \(\mathcal L\) is called span-symmetric if there are two disjoint axes of symmetry. The generalized quadrangle \(Q(4,s)\) arises from a quadric in \(PG(4,s)\).NEWLINENEWLINENEWLINEThe author proves the following theorem: Any span-symmetric generalized quadrangle for which \(t\neq s^2\) is isomorphic to \(Q(4,s)\).