2 problems

Let $G$ be a finite simple group, and let $\Gamma(G)$ denote its Gruenberg–Kegel graph. Vasil'ev's conjecture. There are at most $4$ pairwise non-isomorphic simple groups $H$ such…

Let $G$ be a finite simple group other than $A_6$, and let $\Gamma(G)$ be its Gruenberg–Kegel graph, whose vertices are the prime divisors of $|G|$, with distinct primes adjacent w…