All Questions

Hello! Let $K$ be a number field. All abelian unramified extensions are contained in the Hilbert class field which is a finite extension 'maximal' with respect to this property. For general ...

Let $K \neq \mathbb{Q} $ be a finite extension of $\mathbb{Q}$. For a given integer $n$, how to construct an unramified extension of $K$ of degree $n$ ? EDIT: If not then under what conditions on $K$,...