Maximal subgroups of non-torsion Grigorchuk-Gupta-Sidki groups

TL;DR

This paper extends the understanding of subgroup structures in GGS-groups by showing that non-torsion GGS-groups, including some with weakly regular branch properties, lack maximal subgroups of infinite index.

Contribution

It generalizes previous results from torsion GGS-groups to non-torsion cases, broadening the classification of their subgroup structures.

Findings

Non-torsion GGS-groups do not have maximal subgroups of infinite index.

Includes weakly regular branch GGS-groups in the analysis.

Extends known results from torsion to non-torsion GGS-groups.

Abstract

A Grigorchuk-Gupta-Sidki (GGS-)group is a subgroup of the automorphism group of the $p$-adic tree for an odd prime $p$, generated by one rooted automorphism and one directed automorphism. Pervova proved that all torsion GGS-groups do not have maximal subgroups of infinite index. Here we extend the result to non-torsion GGS-groups, which include the weakly regular branch, but not branch, GGS-group.