Trasformazione di piani affini e insiemi di permutazioni strettamente 2-transitivi planari

In [L.A. Rosati and P.Quattrocchi "Transformation of designs and other incidence structures" geom ded., 44 (1992), pp.233-240] a procedure to transform incidence structures is introduced. Applying this procedure to finite affine planes one obtains an affine plane of the same order. While, when the procedure is applyied to a non finite affine plane a linear incidence structure is obtained but the axiom of parallelism is not assured. In this work we analyze sufficient conditions to transform not finite affine planes into affine planes and not finite planar sharply 2-transitive permutation sets into sharply 2-transitive permutation sets which are still planar.