Showing Galois Group is Abelian I'm having trouble showing that $\text{Gal}(\mathbb{Q}(\zeta_n)/\mathbb{Q})$ is Abelian. First I want to be able to show that $\mathbb{Q}(\zeta_n)/\mathbb{Q}$ is Galois, but I'm also not sure how to do this. Any help is appreciated!

Find the conjugates of $\zeta_n$. If they are all in $\mathbb{Q}(\zeta_n)$, then it's Galois. It may be easier (but in the same spirit) to show that $\mathbb{Q}(\zeta_n)$ is the splitting field of a polynomial.
