Subgroups of free profinite groups and large subfields of Q̃

A. Lubotzky; L. van den Dries

doi:10.1007/BF02762851

Subgroups of free profinite groups and large subfields of Q̃

A. Lubotzky^*
, L. van den Dries

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

We prove that many subgroups of free profinite groups are free, and use this to give new examples of pseudo-algebraically closed subfields of {Mathematical expression} satisfying Hilbert's Irreducibility Theorem, and to solve problems posed by M. Jarden and A. Macintyre. We also find a subfield of {Mathematical expression} which does not satisfy Hilbert's Irreducibility Theorem, but all of whose proper finite extensions do.

Original language	English
Pages (from-to)	25-45
Number of pages	21
Journal	Israel Journal of Mathematics
Volume	39
Issue number	1-2
DOIs	https://doi.org/10.1007/BF02762851
State	Published - Mar 1981
Externally published	Yes

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10.1007/BF02762851

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AB - We prove that many subgroups of free profinite groups are free, and use this to give new examples of pseudo-algebraically closed subfields of {Mathematical expression} satisfying Hilbert's Irreducibility Theorem, and to solve problems posed by M. Jarden and A. Macintyre. We also find a subfield of {Mathematical expression} which does not satisfy Hilbert's Irreducibility Theorem, but all of whose proper finite extensions do.

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Subgroups of free profinite groups and large subfields of Q̃

Abstract

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