I am having an issue classifying $\mathbb{Z}\times\mathbb{Z}/\langle(0,3)\rangle$ according to the fundamental theorem of finitely generated abelian group (i.e. finding what $\mathbb{Z}\times\mathbb{Z}/\langle(0,3)\rangle$ is isomorphic to). I think It should $\mathbb{Z}$, but I am not sure why. Thanks!