abelian extension

Let $K$ be a Galois extension of $F$. The extension is said to be anabelian extension if the Galois group Gal$(K/F)$ is abelian.

Examples: $\mathbb{Q}(\sqrt{2})/\mathbb{Q}$ has Galois group $\mathbb{Z}/2\mathbb{Z}$ so$\mathbb{Q}(\sqrt{2})/\mathbb{Q}$ is an abelian extension.

Let ${\zeta }_n$ be a primitive nth root of unity (http://planetmath.org/RootOfUnity). Then $\mathbb{Q}({\zeta }_n)/\mathbb{Q}$ hasGalois group ${(\mathbb{Z}/n\mathbb{Z})}^{*}$ (the group of units of$\mathbb{Z}/n\mathbb{Z}$) so $\mathbb{Q}({\zeta }_n)/\mathbb{Q}$ is abelian.