3 problems

Folklore conjecture. For any finite group $G$, there exist infinitely many quadratic number fields $K$ such that $K$ possesses a Galois extension with Galois group $G$ unramified a…

Wood's moment conjecture. There exists a number $0<a<1$ such that, for every positive integer $k$,

Wood's conjecture. If there is a unique conjugacy class $c$ of order $2$ elements of $G'$ not contained in $G$, then