2 problems

Fix an odd prime number $p$ and let $K$ be an imaginary quadratic field. Let $G_K$ be the Galois group of the maximal unramified pro-$p$ extension of $K$, called the $p$-tower grou…

Let $G$ be a finitely generated pro-$p$ group. Let $\operatorname{Freq}(G)$ denote its limiting frequency among imaginary quadratic fields, and let $\operatorname{Meas}(G)$ denote…