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An essay on skew translation generalized quadrangles. (English) Zbl 0706.51006

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

MSC:

51E12 Generalized quadrangles and generalized polygons in finite geometry
05B25 Combinatorial aspects of finite geometries
51D20 Combinatorial geometries and geometric closure systems

Citations:

Zbl 0653.51012
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