Realizing residually finite groups as subgroups of branch groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910354172280832 |
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| author | Kionke, Steffen Schesler, Eduard |
| author_facet | Kionke, Steffen Schesler, Eduard |
| contents | We prove that every finitely generated, residually finite group $G$ embeds into a finitely generated perfect branch group $Γ$ such that many properties of $G$ are preserved under this embedding. Among those are the properties of being torsion, being amenable, and not containing a non-abelian free group. As an application we construct a finitely generated, non-amenable torsion branch group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07165 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Realizing residually finite groups as subgroups of branch groups Kionke, Steffen Schesler, Eduard Group Theory 20E08, 43A07, 20E18, 20E26 We prove that every finitely generated, residually finite group $G$ embeds into a finitely generated perfect branch group $Γ$ such that many properties of $G$ are preserved under this embedding. Among those are the properties of being torsion, being amenable, and not containing a non-abelian free group. As an application we construct a finitely generated, non-amenable torsion branch group. |
| title | Realizing residually finite groups as subgroups of branch groups |
| topic | Group Theory 20E08, 43A07, 20E18, 20E26 |
| url | https://arxiv.org/abs/2212.07165 |