Suppose that $H$ and $G$ are groups and that $H \le G$. Prove that if $H \cong \mathbb Z$ or $H \cong \mathbb Z_n$, then $H=\langle g \rangle$ for some $g \in G$
I'm not entirely sure where to go on this problem. I guess if $H= \mathbb Z$, then if for $g=1$, then $H= \langle g \rangle = \langle 1 \rangle$. However, I don't know how to make a general argument.