On the congruence subgroup property for GGS-groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866912001020657664 |
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| author | Fernández-Alcober, Gustavo A. Garrido, Alejandra Uria-Albizuri, Jone |
| author_facet | Fernández-Alcober, Gustavo A. Garrido, Alejandra Uria-Albizuri, Jone |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_03465 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | On the congruence subgroup property for GGS-groups Fernández-Alcober, Gustavo A. Garrido, Alejandra Uria-Albizuri, Jone Group Theory 20E08 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. |
| title | On the congruence subgroup property for GGS-groups |
| topic | Group Theory 20E08 |
| url | https://arxiv.org/abs/1604.03465 |