2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63474We show that for any positive integer $n$ there exists a constant $C(n)>0$ such that any $n$-generated group $G$, which acts by isometries on a $δ$-hyperbolic space (with $δ>0$), is either free or has a nontrivial element with translation length at most $δC(n)$.Group TheoryGeometric Topology20F67text