Find the minimal polynomial of the 18th root of unity and the Galois group of $\mathbb{Q}(z_{18})$ and its generators
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$