2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209181We study finite groups of automorphisms of the $p$-adic open disk. In particular, we generalize results of Green, Matignon and Henrio from cyclic groups of order $p$ to arbitrary finite groups. As an application, we produce a counterexample to a question of Chinburg, Guralnick and Harbater, concerning the local lifting problem for generalized quaternion groups.Remark 4.4 and Lemma 4.5 addedAlgebraic GeometryNumber Theory14H37; 11G20; 14D15text