The automorphism group of a multi-GGS group

TL;DR

This paper computes the automorphism groups of all non-constant multi-GGS-groups, which are automorphism groups of regular rooted trees generalizing Gupta--Sidki p-groups.

Contribution

It provides a complete characterization of automorphism groups for all non-constant multi-GGS-groups, extending previous results on specific cases.

Findings

Automorphism groups are explicitly computed for all non-constant multi-GGS-groups.

The structure of these automorphism groups generalizes known results for Gupta--Sidki p-groups.

The work advances understanding of symmetries in automorphism groups of rooted tree groups.

Abstract

A multi-GGS-group is a group of automorphisms of a regular rooted tree, generalising the Gupta--Sidki $p$-groups. We compute the automorphism groups of all non-constant multi-GGS-groups.