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Generic polynomials for quasi-dihedral, dihedral and modular extensions of order 16


Author: Arne Ledet
Journal: Proc. Amer. Math. Soc. 128 (2000), 2213-2222
MSC (2000): Primary 12F12
DOI: https://doi.org/10.1090/S0002-9939-99-05570-7
Published electronically: December 8, 1999
MathSciNet review: 1707525
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe Galois extensions where the Galois group is the quasi-dihedral, dihedral or modular group of order $16$, and use this description to produce generic polynomials.


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

  • [Bl] E. V. Black, Deformations of Dihedral $2$-Group Extensions of Fields, Trans. Amer. Math. Soc. 351 (1999), 3229-3241. MR 99m:12009
  • [Ja] N. Jacobson, Basic Algebra I, W. H. Freeman and Company, New York, 1985. MR 86d:00001
  • [Ki] I. Kiming, Explicit Classifications of some $2$-Extensions of a Field of Characteristic different from $2$, Canad. J. Math. 42 (1990), 825-855. MR 92c:11115
  • [Le1] A. Ledet, On $2$-Groups as Galois Groups, Canad. J. Math. 47 (1995), 1253-1273. MR 97a:12003
  • [Le2] -, Embedding Problems and Equivalence of Quadratic Forms, Math. Scand. (to appear).
  • [Sa] D. Saltman, Generic Galois Extensions and Problems in Field Theory, Adv. Math. 43 (1982), 250-283. MR 84a:13007

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Additional Information

Arne Ledet
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Email: ledet@mast.queensu.ca

DOI: https://doi.org/10.1090/S0002-9939-99-05570-7
Received by editor(s): September 8, 1998
Published electronically: December 8, 1999
Additional Notes: This work was supported by a Queen’s University Advisory Research Committee Postdoctoral Fellowship.
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society

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