2 problems

Let $p$ be an odd prime, and let the $p$-class tower group of a field $K$ be the Galois group of its maximal unramified $p$-extension, equivalently the pro-$p$ completion of…

Let $D_X$ be the set of imaginary quadratic fields of absolute discriminant less than $X$. For each imaginary quadratic number field $K$, let $\mathcal{G}_K$ be the maximal pro-odd…