The profinite completion of multi-EGS groups

TL;DR

This paper classifies branch multi-EGS groups with the congruence subgroup property, determines their profinite completions, and shows that these groups are just infinite, expanding understanding of their algebraic structure.

Contribution

It provides a classification of branch multi-EGS groups with the congruence subgroup property and explicitly determines their profinite completions, a novel advancement in the study of these groups.

Findings

Branch multi-EGS groups with the congruence subgroup property are classified.

Profinite completions of all branch multi-EGS groups are explicitly determined.

Branch multi-EGS groups are shown to be just infinite.

Abstract

The class of multi-EGS groups is a generalisation of the well-known Grigorchuk-Gupta-Sidki (GGS-)groups. Here we classify branch multi-EGS groups with the congruence subgroup property and determine the profinite completion of all branch multi-EGS groups. Additionally our results show that branch multi-EGS groups are just infinite.