Geodesic
Finitely generated subgroups of free profinite groups and of some Galois groups
Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 95-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {O. V. Mel'nikov},
     title = {Finitely generated subgroups of free profinite groups and of some {Galois} groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {95--106},
     year = {1998},
     volume = {64},
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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/

[1] Karras A., Solitar D., “On finitely generated subgroups of a free group”, Proc. Amer. Math. Soc., 22:1 (1969), 209–213 | DOI | MR | Zbl

[2] Melnikov O. V., “Kharakterizatsiya dostizhimykh podgrupp svobodnykh prokonechnykh grupp”, Dokl. AN BSSR, 22:8 (1978), 677–679 | MR

[3] Melnikov O. V., “Normalnye deliteli svobodnykh prokonechnykh grupp”, Izv. AN SSSR. Ser. matem., 42:1 (1978), 3–25 | MR | Zbl

[4] Lubotzky A., “Combinatorial group theory for pro-$p$-groups”, J. Pure Appl. Algebra, 25 (1982), 311–325 | DOI | MR | Zbl

[5] Hoechsmann K., “Zum Einbettungsproblem”, J. Reine Angew. Math., 229 (1968), 81–106 | MR | Zbl

[6] Uchida K., “Separably Hilbertian fields”, Kodai Math. J., 3:1 (1980), 83–95 | DOI | MR | Zbl

[7] Fried M. D., Jarden M., Field Arithmetic, Springer, Berlin, 1986

[8] Kuyk W., “Extensions de corps hilbertiens”, J. Algebra, 14:1 (1970), 112–124 | DOI | MR | Zbl

[9] Binz E., Neukirch J., Wenzel G. H., “A subgroup theorem for free products of profinite groups”, J. Algebra, 19:1 (1971), 104–109 | DOI | MR | Zbl

[10] Gaschütz W., “Zu einem von B. H. und H. Neumann gestellten Problem”, Math. Nachr., 14:4–6 (1955), 249–252 | DOI | MR