Residually finite groups with uniformly almost flat quotients
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908556095127552 |
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| author | Guo, David Tointon, Matthew |
| author_facet | Guo, David Tointon, Matthew |
| contents | We show that if all the finite coset spaces of a polycyclic group have diameter bounded uniformly below by a polynomial in their size then the group is virtually nilpotent. We obtain the same conclusion for a finitely generated residually torsion-free nilpotent group under the weaker assumption that the finite quotient groups have diameter bounded uniformly below by a polynomial in their size. This extends work of Khukhro and Valette. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23035 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Residually finite groups with uniformly almost flat quotients Guo, David Tointon, Matthew Group Theory Combinatorics We show that if all the finite coset spaces of a polycyclic group have diameter bounded uniformly below by a polynomial in their size then the group is virtually nilpotent. We obtain the same conclusion for a finitely generated residually torsion-free nilpotent group under the weaker assumption that the finite quotient groups have diameter bounded uniformly below by a polynomial in their size. This extends work of Khukhro and Valette. |
| title | Residually finite groups with uniformly almost flat quotients |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2410.23035 |