2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70428The group of affine transformations with rational coefficients, $aff(Q)$, acts naturally on the real line, but also on the $p$-adic fields. The aim of this note is to show that all these actions are necessary and sufficient to represent bounded $μ$-harmonic functions for a probability measure $μ$ on $aff(Q)$ that is supported by a finitely generated sub-group, that is to describe the Poisson boundary.12 pages, 3 figuresProbability60B99, 60J50, 43A05, 22E35text