Embedding finitely presented self-similar groups into finitely presented simple groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913657443581952 |
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| author | Zaremsky, Matthew C. B. |
| author_facet | Zaremsky, Matthew C. B. |
| contents | We prove that every finitely presented self-similar group embeds in a finitely presented simple group. This establishes that every group embedding in a finitely presented self-similar group satisfies the Boone-Higman conjecture. The simple groups in question are certain commutator subgroups of Röver-Nekrashevych groups, and the difficulty lies in the fact that even if a Röver-Nekrashevych group is finitely presented, its commutator subgroup might not be. We also discuss a general example involving matrix groups over certain rings, which in particular establishes that every finitely generated subgroup of $\mathrm{GL}_n(\mathbb{Q})$ satisfies the Boone-Higman conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09722 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embedding finitely presented self-similar groups into finitely presented simple groups Zaremsky, Matthew C. B. Group Theory We prove that every finitely presented self-similar group embeds in a finitely presented simple group. This establishes that every group embedding in a finitely presented self-similar group satisfies the Boone-Higman conjecture. The simple groups in question are certain commutator subgroups of Röver-Nekrashevych groups, and the difficulty lies in the fact that even if a Röver-Nekrashevych group is finitely presented, its commutator subgroup might not be. We also discuss a general example involving matrix groups over certain rings, which in particular establishes that every finitely generated subgroup of $\mathrm{GL}_n(\mathbb{Q})$ satisfies the Boone-Higman conjecture. |
| title | Embedding finitely presented self-similar groups into finitely presented simple groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2405.09722 |