Liftability and Contracting Property of Multi-EGS Groups

TL;DR

This paper establishes conditions under which multi-EGS groups are liftable, producing new examples of transitive groups on regular trees with scale group closures, and explicitly computes their contracting nuclei.

Contribution

It provides new criteria for liftability in multi-EGS groups and computes their contracting nuclei, extending understanding of their structure and properties.

Findings

Multi-EGS groups can be liftable under specific conditions.

Explicit computation of contracting nuclei for these groups.

Identification of new examples of scale groups acting on regular trees.

Abstract

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.