## On the congruence subgroup property for GGS-groups

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- by Gustavo A. Fernández-Alcober, Alejandra Garrido and Jone Uria-Albizuri PDF
- Proc. Amer. Math. Soc.
**145**(2017), 3311-3322 Request permission

## Abstract:

We show that all GGS-groups with a 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 a constant defining vector has an infinite congruence kernel and is not a branch group.## References

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## Additional Information

**Gustavo A. Fernández-Alcober**- Affiliation: Department of Mathematics, University of the Basque Country UPV/EHU, 48080 Bilbao, Spain
- MR Author ID: 307028
- Email: gustavo.fernandez@ehu.eus
**Alejandra Garrido**- Affiliation: Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany
- Email: alejandra.garrido@uni-duesseldorf.de
**Jone Uria-Albizuri**- Affiliation: Department of Mathematics, University of the Basque Country UPV/EHU, 48080 Bilbao, Spain
- Email: jone.uria@ehu.eus
- Received by editor(s): April 12, 2016
- Received by editor(s) in revised form: September 14, 2016
- Published electronically: January 31, 2017
- Additional Notes: The first and third authors acknowledge financial support from the Spanish Government, grants MTM2011-28229-C02 and MTM2014-53810-C2-2-P, and from the Basque Government, grants IT753-13 and IT974-16. The third author was also supported by the Basque Goverment predoctoral grant PRE-2014-1-347. This article was finished while the second author was a postdoctoral researcher at the Université de Genève, whose support and that of the Swiss National Science Foundation she gratefully acknowledges.
- Communicated by: Pham Huu Tiep
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**145**(2017), 3311-3322 - MSC (2010): Primary 20E08
- DOI: https://doi.org/10.1090/proc/13499
- MathSciNet review: 3652785