%0 Journal Article %T Artin characters, Hurwitz trees and the lifting problem %A Louis Hugo Brewis %A Stefan Wewers %J Mathematics %D 2008 %I arXiv %X We 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. %U http://arxiv.org/abs/0810.3603v3