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On vectorial polynomials and coverings in characteristic 3


Authors: Teresa Crespo and Zbigniew Hajto
Journal: Proc. Amer. Math. Soc. 134 (2006), 23-29
MSC (2000): Primary 12F12
DOI: https://doi.org/10.1090/S0002-9939-05-08273-0
Published electronically: August 15, 2005
MathSciNet review: 2170539
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Abstract | References | Similar Articles | Additional Information

Abstract: For $K$ a field containing the finite field $\mathbb{F} _9$ we give explicitly the whole family of Galois extensions of $K$ with Galois group $2S_4*Q_8$ or $2S_4*D_8$ and determine the discriminant of such an extension.


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

  • 1. S.S. Abhyankar, On the ramification of algebraic functions, Amer. J. Math. 77 (1955), 572-592. MR 0071851 (17:193c)
  • 2. S.S. Abhyankar, Local fundamental groups of algebraic varieties, Proc. Amer. Math. Soc. 125 (1997), 1635-1641. MR 1403110 (97h:14032)
  • 3. S.S. Abhyankar, Galois embeddings for linear groups, Trans. Amer. Math. Soc. 352 (2000), 3881-3912. MR 1650057 (2000m:12003)
  • 4. S.S. Abhyankar, Resolution of singularities and modular Galois theory, Bull. Amer. Math. Soc. 38 (2001), 131-169. MR 1816069 (2002a:14013)
  • 5. T. Crespo, $2S_4*Q_8$-extensions in characteristic 3, Proc. Amer. Math. Soc. 132 (2004), 691-695. MR 2019944 (2004j:12003)
  • 6. A. Fröhlich, Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants, J. Reine Angew. Math. 360 (1985), 84-123. MR 0799658 (87h:11028)
  • 7. D. Harbater, M. van der Put and R. Guralnick, Valued fields and covers in characteristic p, Fields Institute Communications 32 (2002), 175-204. MR 1928369 (2003i:12008)
  • 8. T. Y. Lam, The algebraic theory of quadratic forms, Benjamin-Cummings Publ. Co., Reading, MA, 1973. MR 0396410 (53:277)
  • 9. J.-P. Serre, L'invariant de Witt de la forme $\operatorname{Tr}(x^2)$, Comment. Math. Helv. 59 (1984), 651-676. MR 0780081 (86k:11067)
  • 10. E. Witt, Konstruktion von galoischen Körpern der Charakteristik $p$ zu vorgegebener Gruppe der Ordnung $p^f$, J. Reine Angew. Math. 174 (1936), 237-245.

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Additional Information

Teresa Crespo
Affiliation: Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
Email: teresa.crespo@ub.edu

Zbigniew Hajto
Affiliation: Zakład Matematyki, Akademia Rolnicza, al. Mickiewicza 24/28, 30-059 Kraków, Poland
Address at time of publication: Instytut Matematyki, Politechnika Krakowska, ul. Warszawska 24, 31-155 Kraków, Poland
Email: rmhajto@cyf-kr.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-05-08273-0
Received by editor(s): August 4, 2004
Published electronically: August 15, 2005
Additional Notes: This work was partially supported by grant BFM2003-01898, Spanish Ministry of Education
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2005 American Mathematical Society

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