galois theory - Looking for examples of abelian extensions of $mathbb{Q}$ satisfying a certain condition

The Kronecker-Weber Theorem says that every abelian extension of $\mathbb{Q}$ is contained in some cyclotomic extension. One approach to prove this is via higher ramification groups. In this approach, there is a crucial step, which says

Let $K$ be an abelain extension of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=p^m$ and $p$ is the only prime of $\mathbb{Z}$ which ramifies in $K$. To prove the Kronecker-Weber theorem, it is enough to prove that any such $K$ is contained in a cyclotomic extension.

I am looking for some examples such a $K$. Any help ?

Answer

$\Bbb Q(i), \Bbb Q(\sqrt 2), \Bbb Q(\cos(2\pi/9))$ are some examples among many others.