Automorphism groups over Hilbertian fields

François Legrand, Elad Paran

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1-7
Number of pages7
JournalJournal of Algebra
Volume503
DOIs
StatePublished - 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

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