2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223750We describe an algorithm which determines whether or not a group which is hyperbolic relative to abelian groups admits a nontrivial splitting over a finite group.15 pages. Version 2 is 17 pages, edited in light of referee's comments. To appear in Transactions of the AMSGroup Theory20F10; 20F65text