A quantitative Neumann lemma for finitely generated groups
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866914775380787200 |
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| author | Gorokhovsky, Elia Bon, Nicolás Matte Tamuz, Omer |
| author_facet | Gorokhovsky, Elia Bon, Nicolás Matte Tamuz, Omer |
| contents | We study the coset covering function $\mathfrak{C}(r)$ of a finitely generated group: the number of cosets of infinite index subgroups needed to cover the ball of radius $r$. We show that $\mathfrak{C}(r)$ is of order at least $\sqrt{r}$ for all groups. Moreover, we show that $\mathfrak{C}(r)$ is linear for a class of amenable groups including virtually nilpotent and polycyclic groups, and that it is exponential for property (T) groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_11099 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A quantitative Neumann lemma for finitely generated groups Gorokhovsky, Elia Bon, Nicolás Matte Tamuz, Omer Group Theory We study the coset covering function $\mathfrak{C}(r)$ of a finitely generated group: the number of cosets of infinite index subgroups needed to cover the ball of radius $r$. We show that $\mathfrak{C}(r)$ is of order at least $\sqrt{r}$ for all groups. Moreover, we show that $\mathfrak{C}(r)$ is linear for a class of amenable groups including virtually nilpotent and polycyclic groups, and that it is exponential for property (T) groups. |
| title | A quantitative Neumann lemma for finitely generated groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2203.11099 |