Transformation of projective planes and permutation sets

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. Sec. II (1964) 1-18), but does not coincide with it. In the Section 2 we give sufficient conditions to transform a finite (infinity)- l(infinity) transitive projective plane into a plane which is still (infinity)- l(infinity) 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. (C) 1999 Elsevier Science B.V. All rights reserved