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arXiv · 1604.03465

On the congruence subgroup property for GGS-groups

Gustavo A. Fernández-Alcober·Alejandra Garrido·Jone Uria-Albizuri
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Abstract

We show that all GGS-groups with non-constant defining vector satisfy the congruence subgroup property. This provides, for every odd prime $p$, many examples of finitely generated, residually finite, non-torsion groups whose profinite completion is a pro-$p$ group, and among them we find torsion-free groups. This answers a question of Barnea. On the other hand, we prove that the GGS-group with constant defining vector has an infinite congruence kernel and is not a branch group.

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Gustavo A. Fernández-Alcober, Alejandra Garrido, Jone Uria-Albizuri. 2016-04-12. On the congruence subgroup property for GGS-groups. https://doi.org/10.1090/proc/13499

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