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Expansion in ${\text{SL}}_{d}\left(ℤ/qℤ\right)$, $q$ arbitrary. (English) Zbl 1247.20052
Let $S$ be a fixed finite symmetric subset of ${\text{SL}}_{d}\left(ℤ\right)$ that generates a Zariski-dense subgroup $G$. In the current paper it is shown that the Cayley graphs of ${\pi }_{q}\left(G\right)$ with respect to the generating set ${\pi }_{q}\left(S\right)$ form a family of expanders, where ${\pi }_{q}$ denotes the projection map from $ℤ$ onto $ℤ/qℤ$.
##### MSC:
 20G40 Linear algebraic groups over finite fields 20F05 Generators, relations, and presentations of groups 05C25 Graphs and abstract algebra
##### References:
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