2 problems

For a discrete group $G$, let $\mathcal{G}_n(G)$ be the space of epimorphisms $F_n\to G$, equivalently the space of generating $n$-tuples of $G$. The group…

Let $G$ be a finite simple group with $d(G)=2$, where $d(G)$ is the minimum size of a generating set of $G$. For $k\geq 1$, a $T_k$-system is an orbit of generating $k$-tuples unde…