Membership Problem in groups acting freely on -trees

Abstract: Groups acting freely on -trees (-free groups) play a key role in the study of non-archimedean group actions. Following Stallingsʼ ideas, we develop graph-theoretic techniques to investigate subgroup structure of -free groups. As an immediate application of the presented method, we give an effective solution to the Uniform Membership Problem and the Power Problem in -free groups. [Copyright &y& Elsevier]