On transitivity and (non)amenability of Aut(F_n) actions on group presentations

Aglaia Myropolska, Tatiana Nagnibeda

For a finitely generated group $G$ the Nielsen graph $N_n(G)$, $n\ge \mathrm{rank}(G)$, describes the action of the group $\mathrm{Aut}{F}_n$ of automorphisms of the fre…