2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70381Suppose $H$ is a hyperbolic subgroup of a hyperbolic group $G$. Assume there exists $n > 0$ such that the intersection of $n$ essentially distinct conjugates of $H$ is always finite. Further assume $G$ splits over $H$ with hyperbolic vertex and edge groups and the two inclusions of $H$ are quasi-isometric embeddings. Then $H$ is quasiconvex in $G$. This answers a question of Swarup and provides a partial converse to the main theorem of \cite{GMRS}.16 pages, no figures, no tablesGroup TheoryMetric Geometry20F32; 57M50text