3 problems

Consider the product replacement chain on the space of generating $n$-tuples … for a fixed finite group $G$, and let $C_G$ be a constant depending only on $G$. The chain has a unif…

Let $G$ be an infinite group generated by $d$ elements. The main conjecture asserts that the product replacement graphs $\Gamma_k(G)$ have exponential growth for all $k\ge d+1$. If…

Let $F_n$ be a free group and let $G$ be a finite simple group. Write $\operatorname{Epi}(F_n,G)$ for the set of epimorphisms from $F_n$ onto $G$, and let $\mathcal{R}_n(G)$ denote…