Geodesic
Normal subgroups of free profinite groups
Izvestiya. Mathematics, Tome 12 (1978) no. 1, pp. 1-20 
O. V. Mel'nikov. Normal subgroups of free profinite groups. Izvestiya. Mathematics, Tome 12 (1978) no. 1, pp. 1-20. http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a0/
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     author = {O. V. Mel'nikov},
     title = {Normal subgroups of free profinite groups},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We classify up to isomorphism the normal subgroups of free profinite groups and also of their analogues, the so-called free pro-$\Delta$-groups, which include free prosoluble groups and free pro-$\pi$-groups (where $\pi$ is a set of primes). We prove that if $N$ is a normal subgroup of a free СЂРіРѕ-$\Delta$-group, then any proper normal subgroup of $N$ of finite index is a free СЂrРѕ-$\Delta$-group. We find a set of conditions that are comparatively easy to check, which guarantee the freeness of a normal subgroup of a free pro-$\Delta$-group. We discuss the question of when a normal subgroup of a free СЂrРѕ-$\Delta$-group is determined by the set of its finite homomorphic images. Bibliography: 10 titles.

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