Abstract
We show that every finite group occurs as the automorphism group of infinitely many finite (field) extensions of any given Hilbertian field. This extends and unifies previous results of M. Fried and Takahashi on the global field case.
Original language | English |
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Pages (from-to) | 1-7 |
Number of pages | 7 |
Journal | Journal of Algebra |
Volume | 503 |
DOIs | |
State | Published - 1 Jun 2018 |
Bibliographical note
Funding Information:We wish to thank Dan Haran for helpful comments and the anonymous referee for suggesting a more elementary proof of Proposition 2.3 . The first author is partially supported by the Israel Science Foundation (grants No. 693/13 and 577/15 ). The second author is partially supported by the Israel Science Foundation (grant No. 696/13 ).
Keywords
- Automorphism groups
- Hilbertian fields