Groups
Well, on the face of it. since r>n I would have said that therecannot be a surjective relationship, but if say, S_3 ={1 2 3} and C_4 (thus r>n) is
{e, a, a^2, a^3} the order of S_3 is 3! = 6 and the order of C_4 is 4
so there could be a surjective homomorphism. I am stuck at this...