We consider the problem of the classification of semisimple Hopf algebras A
of dimension pq where p <q are two prime numbers. First we prove that the
order of the group of grouplike elements of A is not q, and that if it is p
, then q = 1(mod p). We use it to prove that if A and its dual Hopf algebra
A* are of Frobenius type, then A is either a group algebra or a dual of a
group algebra. Finally, we give a complete classification in dimension 3p,
and a partial classification in dimensions 5p and 7p.