An essay on skew translation generalized quadrangles (Q919267)

The author introduces a notion of Moufang skew translation generalized quadrangle (MSTGQ). This concept includes all known generalized quadrangles with \(s=t^ 2\), except the dual of the translation quadrangle associated with Tits' ovoid. The study of the MSTGQ allows to show that the translation dual of the Gevaert and Johnson generalized quadrangles [\textit{H. Gevaert} and \textit{N. L. Johnson} [Geom. Dedicata 27, 301-317 (1988; Zbl 0653.51012)] are new MSTGQ with \(s=t^ 2\) and \(t=3^ r\) \((r>2)\).