2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163586Let T be a rooted tree and Iso(T) be the group of isometries of T. Using model-theoretic tools we study closed subgroups G of Iso(T) with respect to the number of conjugacy classes of Iso(T) having representatives in G.AMSLaTeX, 30 pagesLogicGroup Theory20A15; 03C45; 20E08; 20E18; 20F45text