Let $G$ be a [cyclic group](/page/Cyclic%20Group). If $G$ is infinite, then $G$ is isomorphic to the additive group $\mathbb{Z}$. If $G$ is finite with $|G| = n$ for some $n \in \mathbb{N}$, then $n \ge 1$ and $G$ is isomorphic to the additive group $\mathbb{Z}/n\mathbb{Z}$.