The general structure of projective planes admitting PSL(2,q)

Projective planes of order n admitting PSL(2, q), q > 3, as a collineation group are investigated for n =<q^2. As a consequence, affine planes of order n admitting PSL(2, q), q > 3, as a collineation group are classifed for n < q^2 and (q; n) <> (5; 16). Finally, a complete classifcation of the translation planes order n that admitting PSL(2, q), q > 3, as a collineation group is obtained for n =< q^2.