The profinite completion of relatively hyperbolic virtually special groups
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917957325553664 |
|---|---|
| author | Zalesskii, Pavel |
| author_facet | Zalesskii, Pavel |
| contents | We give a characterization of toral relatively hyperbolic virtually special groups in terms of the profinite completion. We also prove a Tits alternative for subgroups of the profinite completion $\hat G$ of a relatively hyperbolic virtually compact special group $G$ and completely describe finitely generated pro-$p$ subgroups of $\hat G$. This applies to the profinite completion of the fundamental group of a hyperbolic arithmetic manifold. We deduce that all finitely generated pro-$p$ subgroups of the congruence kernel of a standard arithmetic lattice of $SO(n,1)$ are free pro-$p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_13201 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The profinite completion of relatively hyperbolic virtually special groups Zalesskii, Pavel Group Theory We give a characterization of toral relatively hyperbolic virtually special groups in terms of the profinite completion. We also prove a Tits alternative for subgroups of the profinite completion $\hat G$ of a relatively hyperbolic virtually compact special group $G$ and completely describe finitely generated pro-$p$ subgroups of $\hat G$. This applies to the profinite completion of the fundamental group of a hyperbolic arithmetic manifold. We deduce that all finitely generated pro-$p$ subgroups of the congruence kernel of a standard arithmetic lattice of $SO(n,1)$ are free pro-$p$. |
| title | The profinite completion of relatively hyperbolic virtually special groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2205.13201 |