Membership Problem in Groups Acting Freely on Non-Archimedean Trees.

摘要

Groups acting freely on Zn -trees ( Zn -free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to investigate subgroup structure of Zn -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 Zn -free groups.