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A note on automorphism groups of algebraic number fields


Author: M. Fried
Journal: Proc. Amer. Math. Soc. 80 (1980), 386-388
MSC: Primary 12A55; Secondary 13B10
DOI: https://doi.org/10.1090/S0002-9939-1980-0580989-8
MathSciNet review: 580989
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Abstract | References | Similar Articles | Additional Information

Abstract: For any finite group G the paper gives an explicit and simple construction of (not necessarily Galois) algebraic extensions of Q having their full automorphism group equal to G.


References [Enhancements On Off] (What's this?)

  • [EFrK] E. Fried and J. Kollár, Automorphism groups of algebraic number fields, Math. Z. 163 (1978), 121-123. MR 512465 (80d:14015)
  • [MFr] M. Fried, On Hilbert's irreducibility theorem, J. Number Theory 6 (1974), 211-232. MR 0349624 (50:2117)
  • [Fru] R. Frucht, Herstellung von Graphen mit Vorgegebener abstrakter Gruppe, Compositio Math. 6 (1938), 239-250. MR 1557026
  • [Hi] D. Hilbert, Über die Irreduzibilität ganzer rationaler Functionen, mit ganzzahligen Koeffizienten, Crelles J. Math. 110 (1892), 104-129.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0580989-8
Keywords: Galois theory, Hilbert's irreducibility theorem
Article copyright: © Copyright 1980 American Mathematical Society

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