Regular sets for the affine and projective groups over the field of two elements

In this paper we show that collineation groups of affine and projective spaces over the field of two elements GF (2), except in low dimensions, have regular sets. As an application of this result, we prove that, apart from a finite number of exceptions, any collineation group of affine and projective spaces over GF (2), is geometric. In the exceptional dimensions, all primitive groups are examined.Lavoro eseguito nell'ambito dei finanziamenti del M.P.I. Italia (40%).