2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124624Let T be a k-regular tree (k>2) and A its automorphism group. We analyze a generic finitely generated subgroup Gamma of A. We show that Gamma is free and establish a trichotomy on the closure of Gamma: it is either discrete, compact or has index at most 2 in A.17 pages, 2 figuresGroup Theory20E08; 05C25; 20B15; 20D35text