I have two exercises which are driving me crazy.

1) Is Q finitely generated Z-module?

2) Let . Show, that , where .

I have previously proved that , where G is an Abelian group and , so it's enough to show that . And I have been given the rule . So I have to show that , , is isomorphism.

I have been able to show that this function is homomorphism and injective, but the problem here is how I can show that this function is surjective?