Super approximation for $\text{SL}_2\times \text{SL}_2$ and $\text{ASL}_2$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914525022781440 |
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| author | Tang, Jincheng Zhang, Xin |
| author_facet | Tang, Jincheng Zhang, Xin |
| contents | Let $S\subset \text{SL}_2(\mathbb Z)\times \text{SL}_2(\mathbb Z)$ or $\text{SL}_2(\mathbb Z)\ltimes \mathbb Z^2$ be finite symmetric and assume $S$ generates a group $G$ which is a Zariski-dense subgroup $\text{SL}_2(\mathbb Z)\times \text{SL}_2(\mathbb Z)$ or $\text{SL}_2(\mathbb Z)\ltimes \mathbb Z^2$. We prove that the Cayley graphs $$\{\mathcal Cay(G(\text{mod } q), S (\text{mod } q))\}_{q\in \mathbb Z}$$ form a family of expanders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09982 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Super approximation for $\text{SL}_2\times \text{SL}_2$ and $\text{ASL}_2$ Tang, Jincheng Zhang, Xin Group Theory Combinatorics Dynamical Systems Number Theory 05E18 Let $S\subset \text{SL}_2(\mathbb Z)\times \text{SL}_2(\mathbb Z)$ or $\text{SL}_2(\mathbb Z)\ltimes \mathbb Z^2$ be finite symmetric and assume $S$ generates a group $G$ which is a Zariski-dense subgroup $\text{SL}_2(\mathbb Z)\times \text{SL}_2(\mathbb Z)$ or $\text{SL}_2(\mathbb Z)\ltimes \mathbb Z^2$. We prove that the Cayley graphs $$\{\mathcal Cay(G(\text{mod } q), S (\text{mod } q))\}_{q\in \mathbb Z}$$ form a family of expanders. |
| title | Super approximation for $\text{SL}_2\times \text{SL}_2$ and $\text{ASL}_2$ |
| topic | Group Theory Combinatorics Dynamical Systems Number Theory 05E18 |
| url | https://arxiv.org/abs/2308.09982 |