Finitely generated subgroups of free profinite groups and of some Galois groups

O. V. Mel'nikov

Belarusian State University

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 $[F:H]<\infty$.

UDC: 512.546+512.623

Received: 15.04.1997

DOI: 10.4213/mzm1375

 English version: Mathematical Notes, 1998, 64:1, 82–91

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