Payne, Stanley E. An essay on skew translation generalized quadrangles. (English) Zbl 0706.51006 Geom. Dedicata 32, No. 1, 93-118 (1989). 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 [H. Gevaert and N. L. Johnson [Geom. Dedicata 27, 301-317 (1988; Zbl 0653.51012)] are new MSTGQ with \(s=t^ 2\) and \(t=3^ r\) \((r>2)\). Reviewer: C.Lefevre-Percsy Cited in 5 ReviewsCited in 37 Documents MSC: 51E12 Generalized quadrangles and generalized polygons in finite geometry 05B25 Combinatorial aspects of finite geometries 51D20 Combinatorial geometries and geometric closure systems Keywords:Moufang skew translation generalized quadrangle Citations:Zbl 0653.51012 PDFBibTeX XMLCite \textit{S. E. Payne}, Geom. Dedicata 32, No. 1, 93--118 (1989; Zbl 0706.51006) Full Text: DOI