Let $G$ be a group.

For $g\in G$, let $\langle g\rangle=\{g^n\mid n\in{\mathbb Z}\}$ be the cyclic subgroup generated by $g$.

The order of $h\in G$ is the order of the cyclic subgroup $\langle h\rangle$ it generates.

For example,

ifthe group $({\mathbb Z}/m{\mathbb Z})^\ast$ of residue classes mod $m$ of the integers coprime to $m$ is cyclic, a generator is called a primitive root mod $m$, and the existence of a primitive root mod $m$ of course implies that $({\mathbb Z}/m{\mathbb Z})^\ast$ is cyclic.

Which of the following is correct? You don't need a calculator.