3 problems

Let $G$ be a finite simple group and let $A\subseteq G$ be a subset with $|A|\geq 2$. A conjugate of $A$ means a set $gAg^{-1}$ for some $g\in G$. Liebeck–Nikolov–Shalev conjecture…

Ore--Thompson conjecture. For every finite simple group $G$, $\operatorname{or}(G)=2$. The conjecture concerns products of elements from a single conjugacy class and is used in the…

Product conjecture. If $\Gamma$ and $\Gamma'$ are graphically discrete, then