A quantitative Neumann lemma for finitely generated groups
| Autor: | Gorokhovsky, Elia, Bon, Nicolás Matte, Tamuz, Omer |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Israel Journal of Mathematics, 2024 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11856-024-2617-x |
| Popis: | 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. Comment: 12 pages |
| Databáze: | arXiv |
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