Embedding problems for automorphism groups of field extensions

Arno Fehm, François Legrand, Elad Paran

Research output: Contribution to journalArticlepeer-review


A central conjecture in inverse Galois theory, proposed by Dèbes and Deschamps, asserts that every finite split embedding problem over an arbitrary field can be regularly solved. We give an unconditional proof of a consequence of this conjecture, namely that such embedding problems can be regularly solved if one waives the requirement that the solution fields are normal. This extends previous results of M. Fried, Takahashi, Deschamps and the last two authors concerning the realization of finite groups as automorphism groups of field extensions.

Original languageEnglish
Pages (from-to)732-744
Number of pages13
JournalBulletin of the London Mathematical Society
Issue number4
StatePublished - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019 London Mathematical Society


  • 12E25
  • 12E30
  • 12F12
  • 20B25 (primary)


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