Uniform almost flatness in finitely generated soluble groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917417891921920 |
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| author | Guo, David |
| author_facet | Guo, David |
| contents | We show that a finitely generated soluble group is virtually nilpotent if and only if the diameter of its finite coset spaces admits a uniform polynomial lower bound in terms of their size. We obtain the same conclusion for certain finitely generated abelian-by-cyclic groups under the weaker assumption that the diameters of their finite quotients are uniformly bounded below by a polynomial in their size. This extends the previous work of the author with Tointon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16866 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform almost flatness in finitely generated soluble groups Guo, David Group Theory Combinatorics We show that a finitely generated soluble group is virtually nilpotent if and only if the diameter of its finite coset spaces admits a uniform polynomial lower bound in terms of their size. We obtain the same conclusion for certain finitely generated abelian-by-cyclic groups under the weaker assumption that the diameters of their finite quotients are uniformly bounded below by a polynomial in their size. This extends the previous work of the author with Tointon. |
| title | Uniform almost flatness in finitely generated soluble groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2604.16866 |