3 problems

Multiplicativity conjecture. For any two such groups,

Farrokhi–Safa's weaker conjecture. Every finite group $G$ satisfies

Farrokhi–Safa's conjecture. If $d(H,G)=d_k$, then $|H/Z(H,G)|$ is a product of at most $k$ primes. Consequently, $|G/Z(G)|$ is a product of at most $|\mathcal{D}(G)|-1$ primes.