Q: Let G, H be cyclic groups, generated by elements x, y. Determine the condition on the orders m,n of x and y so that the map sending x^i --> y^i is a group homomorphism.
Ans: For m<n a function which sends x^i --> y^i can not be well defined; but for m>or=n there is no such problem.
So, the required condition is m > or = n.
AM I RIGHT?