2 problems

Let $m\geq 3$, and let $q(4m)$ denote the number of braces $B$ whose multiplicative group $(B,\circ)$ is a generalised quaternion group of order $4m$. Guarnieri–Vendramin's conject…

Guarnieri–Vendramin's conjecture. If $p$ and $q$ are primes such that $p<q$ and $p\nmid q-1$, then