14.18 (1999)

We say that a family of groups $\mathscr{D}$ discriminates a group $G$ if for any finite subset $\{a_1, \dots, a_n\} \subseteq G \setminus \{1\}$ there exists a group $D \in \mathscr{D}$ and a homomorphism $\varphi : G \to D$ such that $a_j\varphi \neq 1$ for all $j = 1, \dots, n$. Is every finitely generated group acting freely on some $\Lambda$-tree discriminated by torsion-free hyperbolic groups?