Sharply 1-transitive subsets of certain permutation groups

In this paper we give a method for constructing sharply 1-transitive permutation sets inside a finite permutation group with certain properties and we apply this method to obtain a family of sharply 1-transitive permutation subsets of the sharply 3-transitive permutation group M(p^2f) on PG(1, p^2f) for p^f 1 (mod 4).Work supported by G.N.S.A.G.A. and M.P.I.