3 problems

Đoković's conjecture. Every simple real Lie group has commutator length $1$.

Let $g\geq 3$ and let $\mathcal M_g$ be the mapping class group of a closed orientable surface of genus $g$. A group $G$ is uniformly perfect if there is a natural number $N$ such…

Let $S$ be a closed nonorientable surface and let $c$ be a two-sided simple closed curve such that either $c$ is nonseparating and the genus of $S$ is $7$, or the genus of $S$ is…