Automorphism groups over Hilbertian fields

François Legrand; Elad Paran

doi:10.1016/j.jalgebra.2017.12.041

Automorphism groups over Hilbertian fields

François Legrand, Elad Paran

Mathematics discipline

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1-7
Number of pages	7
Journal	Journal of Algebra
Volume	503
DOIs	https://doi.org/10.1016/j.jalgebra.2017.12.041
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

Access to Document

10.1016/j.jalgebra.2017.12.041

Cite this

@article{d7e282b0d59a46c8823b22b50ab03f80,

title = "Automorphism groups over Hilbertian fields",

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.",

keywords = "Automorphism groups, Hilbertian fields",

author = "Fran{\c c}ois Legrand and Elad Paran",

year = "2018",

month = jun,

day = "1",

doi = "10.1016/j.jalgebra.2017.12.041",

language = "אנגלית",

volume = "503",

pages = "1--7",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Automorphism groups over Hilbertian fields

AU - Legrand, François

AU - Paran, Elad

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - Automorphism groups

KW - Hilbertian fields

UR - http://www.scopus.com/inward/record.url?scp=85044582564&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.12.041

DO - 10.1016/j.jalgebra.2017.12.041

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85044582564

SN - 0021-8693

VL - 503

SP - 1

EP - 7

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Automorphism groups over Hilbertian fields

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this