A Quantitative Selberg's Lemma
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914687427280896 |
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| author | Gelander, Tsachik Slutsky, Raz |
| author_facet | Gelander, Tsachik Slutsky, Raz |
| contents | We show that an arithmetic lattice $Γ$ in a semi-simple Lie group $G$ contains a torsion-free subgroup of index $δ(v)$ where $v = μ(G/Γ)$ is the co-volume of the lattice. We prove that $δ$ is polynomial in general and poly-logarithmic under GRH. We then show that this poly-logarithmic bound is almost optimal, by constructing certain lattices with torsion elements of order $\sim \frac{\log v}{\log \log v}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15976 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Quantitative Selberg's Lemma Gelander, Tsachik Slutsky, Raz Group Theory 22E40, 20G30, 20H05 We show that an arithmetic lattice $Γ$ in a semi-simple Lie group $G$ contains a torsion-free subgroup of index $δ(v)$ where $v = μ(G/Γ)$ is the co-volume of the lattice. We prove that $δ$ is polynomial in general and poly-logarithmic under GRH. We then show that this poly-logarithmic bound is almost optimal, by constructing certain lattices with torsion elements of order $\sim \frac{\log v}{\log \log v}$. |
| title | A Quantitative Selberg's Lemma |
| topic | Group Theory 22E40, 20G30, 20H05 |
| url | https://arxiv.org/abs/2311.15976 |