2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165020We prove that if $G$ is a free-torsion group and $w(t)$ is a word in the alphabet $G \sqcup \{t^{\pm 1}\}$ with exponent sum one, then the group $<G,t|(w(t))^k = 1>$, where $k \geq 2$, is relatively hyperbolic with respect to $G$.10 pages, 7 figuresGroup TheoryAlgebraic Geometry20F05,20F10text