The $\text{units}$ in a ring of integers are those elements whose multiplicative inverse exists. That is, $u$ is unit if $u^{-1}$ also exists in the ring such that $uu^{(-1)}=u^{(-1)}u=\text{multiplicative identity}$.
For example, consider the ring of integers $\mathbb{Z}$ of the rational field $\mathbb{Q}$, then $\mathbb{Z}^{\times}=$ units in $\mathbb{Z}=\{1,-1 \}.$ This is a cyclic group. In fact, this is trivial and $\mathbb{Z}$ is infinite cyclic group.
Now consider the ring of integers $\mathcal{O}_K$ in a finite extension $K \supset \mathbb{Q}$ or the ring of integers $\mathcal{O}_K$ of $p$-adic field $K \supset \mathbb{Q}_p$.
Now denote the units of $\mathcal{O}_K$ by $\mathcal{O}_K^{\times}$.
Is $\mathcal{O}_K^{\times}$ a cyclic group just like $\mathbb{Z}^{\times}$ ?