Splitting field of $x^m-1$ over $\QQ$ and its Galois group

The $m$th roots of unity generate $\QQ(\zeta_m)$, whose Galois group is $(\ZZ/m\ZZ)^\times$.Suggest a slogan

Let $m \geq 1$ and let $\zeta_m$ be a primitive $m$th root of unity in $\CC$. The splitting field of $x^m - 1$ over $\QQ$ is the cyclotomic field $\QQ(\zeta_m)$, and \[ \Gal(\QQ(\zeta_m)/\QQ) \cong \unitsof{(\ZZ/m\ZZ)}. \]