Abstract
We classify up to isomorphism the normal subgroups of free profinite groups and also of their analogues, the so-called free pro-Δ-groups, which include free prosoluble groups and free pro-π-groups (where π is a set of primes). We prove that if N is a normal subgroup of a free pro-Δ-group, then any proper normal subgroup of N of finite index is a free pro-Δ-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-Δ-group. We discuss the question of when a normal subgroup of a free pro-Δ-group is determined by the set of its finite homomorphic images.Bibliography: 10 titles.
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