Transformation of projective planes and permutation sets

Abstract

A new method for transforming incidence structures and sharply multiply transitive permutation sets was introduced in Quattrocchi and Rosati (Geom. Dedicata 44 (1992) 233–240). When applied to projective planes this method resembles Ostrom's derivation technique, (Ostrom, Trans. Amer. Math. Soc. 11 (1964) 1–18), but does not coincide with it. In the Section 2 we give sufficient conditions to transform a finite (∞)−l ∞ transitive projective plane into a plane which is still (∞)−l ∞ transitive. Furthermore, we apply the transformation method to the construction of flocks (i.e. sharply 1-transitive permutation sets). In the Section 3 we refine the transformation method of Quattrocchi and Rosati (Geom. Dedicata 44 (1992) 233–240) and obtain a reversible transformation procedure.