Geodesic
Finitely generated subgroups of free profinite groups and of some Galois groups
Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 95-106.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that, for a (closed) subgroup $H$ of a free profinite or free prosolvable group $F$ of $\operatorname{rank}F>1$ such that $H$ contains a nontrivial composition subgroup $N$ of $F$, we have $\operatorname{rank}F\infty$ and $[F:H]\infty$. 
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     title = {Finitely generated subgroups of free profinite groups and of some {Galois} groups},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a9/}
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O. V. Mel'nikov. Finitely generated subgroups of free profinite groups and of some Galois groups. Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 95-106. http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a9/

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