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A note on the quaternion group as Galois group


Author: Roger Ware
Journal: Proc. Amer. Math. Soc. 108 (1990), 621-625
MSC: Primary 12F10; Secondary 11E81
DOI: https://doi.org/10.1090/S0002-9939-1990-0998741-4
MathSciNet review: 998741
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Abstract: The occurrence of the quaternion group as a Galois group over certain fields is investigated. A theorem of Witt on quaternionic Galois extensions plays a key role.


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

  • [1] J. Arason, R. Elman and B. Jacob, Rigid elements, valuations and realizations of Witt rings, J. Algebra 110 (1987), 449-467. MR 910395 (89a:11041)
  • [2] A. Fröhlich, Orthogonal representation of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants, J. Reine Angew. Math. 360 (1985), 84-123. MR 799658 (87h:11028)
  • [3] B. Jacob and R. Ware, A recursive description of the maximal pro-$ 2$-Galois group via Witt rings, Math. Z. 200 (1989), 379-396. MR 978598 (90b:11127)
  • [4] T. Y. Lam, The algebraic theory of quadratic forms, Benjamin, Elmsford, New York, 1973. MR 0396410 (53:277)
  • [5] J. Minač, Quaternion fields inside the Pythagorean closure, J. Pure Appl. Algebra 57 (1989), 79-82. MR 984048 (90b:11033)
  • [6] J.-P. Serre, L'invariant de Witt de la Forme $ Tr\left( {{x^2}} \right)$, Comment Math. Helv. 59 (1984), 651-676. MR 780081 (86k:11067)
  • [7] R. Ware, When are Witt rings group rings? II, Pacific J. Math. 76 (1978), 541-564. MR 0568320 (58:27920)
  • [8] -, Quadratic forms and pro-$ 2$-groups II: the Galois group of the Pythagorean closure of a formally real field, J. Pure Appl. Algebra 30 (1983), 95-107. MR 716238 (85f:11028)
  • [9] E. Witt, Konstruktion von galoisschen Körpen der Charakteristik $ p$ zu vorgegebener Gruppe der Ordnung $ {p^f}$, J. Reine Angew. Math. 174 (1936), 237-245.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-0998741-4
Article copyright: © Copyright 1990 American Mathematical Society

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