3 problems

Let $F_2=\langle x,y\rangle$ be the free group of rank two, and let $u(x,y),v(x,y)$ be normal generators of $F_2$. For a finite factor group $G$ of $F_2$, write $\bar x,\bar y$ and…

Let $G$ be a black box group and let $N\lhd G$. The Andrews--Curtis graph $\Delta_k(G,N)$ supports a nearest-neighbour random walk, and the AC-replacement algorithm $ACR_k(G,N)$ ru…

Let $F_k$ be the free group of rank $k$. For a group $G$ and a normal subgroup $N\lhd G$, let $V_k(G,N)$ be the set of $k$-tuples that generate $N$ as a normal subgroup of $G$, and…