Multi-GGS-groups have the congruence subgroup property

TL;DR

This paper extends the congruence subgroup property to a broader class of multi-GGS-groups, showing most possess this property except a specific constant vector case, requiring new proof techniques.

Contribution

It generalizes the congruence subgroup property to multi-GGS-groups beyond the original GGS-groups, with novel ideas for the proof.

Findings

All multi-GGS-groups except the constant vector case have the congruence subgroup property.

New proof techniques are developed to handle the generalization.

The result broadens understanding of subgroup structures in these groups.

Abstract

We generalize the result about the congruence subgroup property for GGS-groups to the family of multi-GGS-groups; that is, all multi-GGS-groups except the one defined by the constant vector have the congruence subgroup property. Even if the result remains, new ideas are needed in order to generalize the proof.