Geodesic
Word maps, conjugacy classes, and a noncommutative Waring-type theorem
Aner Shalev1
1 The Hebrew University of Jerusalem<br/>Einstein Institute of Mathematics<br/>91904 Jerusalem<br/>Israel
Annals of mathematics, Tome 170 (2009) no. 3, pp. 1383-1416.

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

Let $w = w(x_1,\ldots , x_d) \ne 1$ be a nontrivial group word. We show that if $G$ is a sufficiently large finite simple group, then every element $g \in G$ can be expressed as a product of three values of $w$ in $G$. This improves many known results for powers, commutators, as well as a theorem on general words obtained in [19]. The proof relies on probabilistic ideas, algebraic geometry, and character theory. Our methods, which apply the `zeta function’ $\zeta_G(s) = \sum_{\chi \in {\rm Irr}\, G} \chi(1)^{-s}$, give rise to various additional results of independent interest, including applications to conjectures of Ore and Thompson.
DOI : 10.4007/annals.2009.170.1383

Aner Shalev 1

1 The Hebrew University of Jerusalem<br/>Einstein Institute of Mathematics<br/>91904 Jerusalem<br/>Israel 
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Aner Shalev. Word maps, conjugacy classes, and a noncommutative Waring-type theorem. Annals of mathematics, Tome 170 (2009) no. 3, pp. 1383-1416. doi : 10.4007/annals.2009.170.1383. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.1383/

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