The super approximation property of $\mathrm{SL}_2(\mathbb{Z}/q\mathbb{Z}) \times \mathrm{SL}_2(\mathbb{Z}/q\mathbb{Z}) \times \mathrm{SL}_2(\mathbb{Z}/q\mathbb{Z})$
| Autor: | Zhang, Chong |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Take $S \subset \mathrm{SL}_2(\mathbb{Z}) \times \mathrm{SL}_2(\mathbb{Z})\times \mathrm{SL}_2(\mathbb{Z})$ be finite symmetric and assume $S$ generates a group $G$ which is Zariski-dense in $\mathrm{SL}_2 \times \mathrm{SL}_2\times \mathrm{SL}_2(\mathbb{Z})$. This paper proves that the Cayley graphs $$ \{\mathcal{C} a y(G(\bmod q), S(\bmod q))\}_{q \in \mathbb{Z}_{+}} $$ form a family of expanders. Comment: arXiv admin note: substantial text overlap with arXiv:2308.09982 by other authors |
| Databáze: | arXiv |
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