Non-closed subgroups of weakly branch groups
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908665427001344 |
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| author | Fariña-Asategui, Jorge Leemann, Paul-Henry Nagnibeda, Tatiana |
| author_facet | Fariña-Asategui, Jorge Leemann, Paul-Henry Nagnibeda, Tatiana |
| contents | For a weakly branch group $G$ acting on a regular enough rooted tree, we provide two constructions of continuous families of distinct subgroups that are not closed in the profinite topology on $G$. On the one hand, we construct a continuous family of distinct non-closed subgroups such that each $H$ in the family is not ERF, that is, contains subgroups not closed in the profinite topology on $H$. On the other hand, under an additional assumption on $G$, we construct a continuous family of ERF subgroups which are not closed in the congruence (and in the profinite) topology on $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-closed subgroups of weakly branch groups Fariña-Asategui, Jorge Leemann, Paul-Henry Nagnibeda, Tatiana Group Theory Primary: 20E08, 20E26, Secondary: 20E18, 20E07 For a weakly branch group $G$ acting on a regular enough rooted tree, we provide two constructions of continuous families of distinct subgroups that are not closed in the profinite topology on $G$. On the one hand, we construct a continuous family of distinct non-closed subgroups such that each $H$ in the family is not ERF, that is, contains subgroups not closed in the profinite topology on $H$. On the other hand, under an additional assumption on $G$, we construct a continuous family of ERF subgroups which are not closed in the congruence (and in the profinite) topology on $G$. |
| title | Non-closed subgroups of weakly branch groups |
| topic | Group Theory Primary: 20E08, 20E26, Secondary: 20E18, 20E07 |
| url | https://arxiv.org/abs/2511.15277 |