Abstract
It is proved that, for a (closed) subgroupH of a free profinite or free prosolvable groupF of rankF>1 such thatH contains a nontrivial composition subgroupN ofF, we have rankF<∞ and [F:H]<∞.
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Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 95–106, July, 1998.
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Mel'nikov, O.V. Finitely generated subgroups of free profinite groups and of some Galois groups. Math Notes 64, 82–91 (1998). https://doi.org/10.1007/BF02307198
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DOI: https://doi.org/10.1007/BF02307198