Abstract
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 language | English |
---|---|
Pages (from-to) | 732-744 |
Number of pages | 13 |
Journal | Bulletin of the London Mathematical Society |
Volume | 51 |
Issue number | 4 |
DOIs | |
State | Published - 1 Aug 2019 |
Bibliographical note
Publisher Copyright:© 2019 London Mathematical Society
Keywords
- 12E25
- 12E30
- 12F12
- 20B25 (primary)