Geodesic
Growth and generation in $\mathrm{SL}_2(\mathbb{Z}/p \mathbb{Z})$
Harald A. Helfgott1
1 Department of Mathematics<br/>University of Bristol<br/>Bristol BS8 1TW<br/>United Kingdom
Annals of mathematics, Tome 167 (2008) no. 2, pp. 601-623.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We show that every subset of $\mathrm{SL}_2(\mathbb{Z}/p\mathbb{Z})$ grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators $A$ of $\mathrm{SL}_2(\mathbb{Z}/p\mathbb{Z})$, every element of $\mathrm{SL}_2(\mathbb{Z}/p\mathbb{Z})$ can be expressed as a product of at most $O((\log p)^c)$ elements of $A \cup A^{-1}$, where $c$ and the implied constant are absolute.
DOI : 10.4007/annals.2008.167.601

Harald A. Helfgott 1

1 Department of Mathematics<br/>University of Bristol<br/>Bristol BS8 1TW<br/>United Kingdom 
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Harald A. Helfgott. Growth and generation in $\mathrm{SL}_2(\mathbb{Z}/p \mathbb{Z})$. Annals of mathematics, Tome 167 (2008) no. 2, pp. 601-623. doi : 10.4007/annals.2008.167.601. http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.167.601/

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