Mild pro-$p$-groups and $p$-extensions of imaginary quadratic fields with non-trivial $p$-class group

Zakariae Bouazzaoui, Abdelaziz El Habibi

Let $k$ be an imaginary quadratic field and $p$ an odd prime number such that the $p$-rank of the class group of $k$ is one. Let $S$ be a finite set of places of $k$ distinct from…