Let be a generator of your cyclic group , can you find a function such that and such that is an homomorphism?
if is to be a homomorphism, we must have f(a*a) = f(a) + f(a) = 1+1. so there is really only "one" essential way to define f:
. that f is a homomorphism follows immediately from the laws of exponents.
since G is finite it suffices to show that f is surjective (clearly |G| = = n), and thus f is an isomorphism.