Liftability and Contracting Property of Multi-EGS Groups

We provide sufficient conditions for the multi-EGS groups to be liftable and thus produce new examples of groups acting transitively on regular trees of finite degree stabilizing one of the ends, whose closures are scale groups as defined by Willis. Additionally, we explicitly compute the contracting nuclei of the groups in this class. We also specialize our results to the classes of multi-edge spinal group and EGS-groups.