Example 5

For every integer $n >$ 0, let us denote by $\mu_n$ the group of $n$th roots of unity in $\mathbf{C}$ (A, V, p. 75). The mapping $z\mapsto z^n$ makes $\mathbf{C}^*$ into a principal covering of $\mathbf{C}^*$ with group $\mu_n$, this group operating in $\mathbf{C}^*$ by multiplication.