In their first article, the authors initiated a systematic study of hyperbolic $\Lambda$-metric spaces, where $\Lambda$ is an ordered abelian group, and groups acting on such spaces. The present paper concentrates on the case $\Lambda = \mathbf{ Z}^n$ taken with the right lexicographic order and studies the structure of finitely generated groups acting on hyperbolic $\mathbf{ Z}^n$-metric spaces. Under certain constraints, the structure of such groups is described in terms of a { \em hierarchy} similar to the one established for $\mathbf{ Z}^n$-free groups by Kharlampovich, Myasnikov, Remeslennikov and Serbin.
Categories: math.GR