Geodesic
On finitely generated profinite groups, I: strong completeness and uniform bounds
Nikolay Nikolov1 ; Dan Segal2
1 New College, Oxford University, Oxford OX1 3BN, United Kingdom
2 All Souls College, Oxford University, Oxford OX1 4AL, United Kingdom
Annals of mathematics, Tome 165 (2007) no. 1, pp. 171-238.

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

We prove that in every finitely generated profinite group, every subgroup of finite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is deduced from the main result about finite groups: let $w$ be a `locally finite’ group word and $d\in\mathbb{N}$. Then there exists $f=f(w,d)$ such that in every $d$-generator finite group $G$, every element of the verbal subgroup $w(G)$ is equal to a product of $f$ $w$-values.
DOI : 10.4007/annals.2007.165.171

Nikolay Nikolov 1 ; Dan Segal 2

1 New College, Oxford University, Oxford OX1 3BN, United Kingdom
2 All Souls College, Oxford University, Oxford OX1 4AL, United Kingdom 
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Nikolay Nikolov; Dan Segal. On finitely generated profinite groups, I: strong completeness and uniform bounds. Annals of mathematics, Tome 165 (2007) no. 1, pp. 171-238. doi : 10.4007/annals.2007.165.171. http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.171/

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