2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73237Let $G$ be a group endowed with a solution to the conjugacy problem and with an algorithm which computes the centralizer in $G$ of any element of $G$. Let $H$ be a subgroup of $G$. We give some conditions on $H$, under which we provide a solution to the conjugacy problem in $H$. We apply our results to some Artin groups and braid type groups. In particular, we give explicit solutions to the conjugacy problem in the Artin groups of type $\tilde{A}_n$ and $\tilde{C}_n$.9 pages, 4 figuresGroup Theory20F36 (Primary), 20F10 (Secondary)text