Subgroups of free profinite groups and large subfields of {Mathematical expression}

A. Lubotzky, L. van den Dries

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)25-45
Number of pages21
JournalIsrael Journal of Mathematics
Issue number1-2
StatePublished - Mar 1981
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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