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Matematicheskie Zametki, 1998, Volume 64, Issue 1, Pages 95–106
DOI: https://doi.org/10.4213/mzm1375 (Mi mzm1375) 		 
Finitely generated subgroups of free profinite groups and of some Galois groups

O. V. Mel'nikov

Belarusian State University
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DOI: https://doi.org/10.4213/mzm1375
Abstract: 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 $[F:H]<\infty$.
Received: 15.04.1997
English version:
Mathematical Notes, 1998, Volume 64, Issue 1, Pages 82–91
DOI: https://doi.org/10.1007/BF02307198
Bibliographic databases:
UDC: 512.546+512.623
Language: Russian
Citation: O. V. Mel'nikov, “Finitely generated subgroups of free profinite groups and of some Galois groups”, Mat. Zametki, 64:1 (1998), 95–106; Math. Notes, 64:1 (1998), 82–91
Citation in format AMSBIB
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\jour Math. Notes
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\vol 64
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\pages 82--91
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