Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. (Q421012)
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scientific article; zbMATH DE number 6037975
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. |
scientific article; zbMATH DE number 6037975 |
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Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. (English)
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23 May 2012
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Let \(S\) be a fixed finite symmetric subset of \(\text{SL}_d(\mathbb Z)\) that generates a Zariski-dense subgroup \(G\). In the current paper it is shown that the Cayley graphs of \(\pi_q(G)\) with respect to the generating set \(\pi_q(S)\) form a family of expanders, where \(\pi_q\) denotes the projection map from \(\mathbb Z\) onto \(\mathbb Z/q\mathbb Z\).
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Cayley graphs
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Zariski-dense subgroups
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expander families
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generating sets
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special linear groups
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expansions
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0.9165926
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0.8503837
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0.8438339
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0.84330666
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0.83455527
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0.8285526
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0.82541853
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