Geodesic
Normal subgroups of free profinite groups
Izvestiya. Mathematics , Tome 12 (1978) no. 1, pp. 1-20

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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 рго-$\Delta$-group, then any proper normal subgroup of $N$ of finite index is a free рrо-$\Delta$-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 рrо-$\Delta$-group is determined by the set of its finite homomorphic images. Bibliography: 10 titles. 
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     author = {O. V. Mel'nikov},
     title = {Normal subgroups of free profinite groups},
     journal = {Izvestiya. Mathematics },
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     number = {1},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a0/}
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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/