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Field Theory

Extensions and Galois Theory

12Fxx

[1] Alejandro Adem, Wenfeng Gao, Dikran B. Karagueuzian, and Ján Mináč. Field theory and the cohomology of some Galois groups. J. Algebra, 235(2):608–635, 2001.
[2] Bill Allombert. An efficient algorithm for the computation of Galois automorphisms. Math. Comp., 73(245):359–375 (electronic), 2004.
[3] Johan Bosman. A polynomial with Galois group SL2(F16). arXiv:math/0701442, 7 pages, 2007.
[4] Nigel Boston. Reducing the Fontaine-Mazur conjecture to group theory. In Progress in Galois theory, volume 12 of Dev. Math., pages 39–50. Springer, New York, 2005.
[5] Nigel Boston and Charles Leedham-Green. Explicit computation of Galois p-groups unramified at p. J. Algebra, 256(2):402–413, 2002.
[6] Nigel Boston and Harris Nover. Computing pro-p-Galois groups. In Algorithmic Number Theory, volume 4076 of Lecture Notes in Comput. Sci., pages 1–10. Springer, Berlin, 2006.
[7] Nigel Boston and David Perry. Maximal 2-extensions with restricted ramification. J. Algebra, 232(2):664–672, 2000.
[8] Antoine Colin. Relative resolvents and partition tables in Galois group computations. In Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), pages 78–84 (electronic), New York, 1997. ACM.
[9] Pilar Fernandez-Ferreiros and M. Angeles Gomez-Molleda. Deciding the nilpotency of the Galois group by computing elements in the centre. Math. Comp., 73(248):2043–2060 (electronic), 2004.
[10] Louis Granboulan. Construction d'une extension régulière de Q(T) de groupe de Galois M24. Experiment. Math., 5(1):3–14, 1996.
[11] Farshid Hajir. On the Galois group of generalized Laguerre polynomials. J. Théor. Nombres Bordeaux, 17(2):517–525, 2005.
[12] Farshid Hajir. Tame pro-p Galois groups: A survey of recent work. In Arithmetic, Geometry and Coding Theory (AGCT 2003), volume 11 of Sémin. Congr., pages 111–124. Soc. Math. France, Paris, 2005.
[13] G. Hanrot and F. Morain. Solvability by radicals from an algorithmic point of view. In Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, pages 175–182 (electronic), New York, 2001. ACM.
[14] Gregor Kemper and Gunter Malle. Invariant fields of finite irreducible reflection groups. Math. Ann., 315(4):569–586, 1999.
[15] Jürgen Klüners and Gunter Malle. Explicit Galois realization of transitive groups of degree up to 15. J. Symbolic Comput., 30(6):675–716, 2000.
[16] Jörn Müller-Quade and Rainer Steinwandt. Recognizing simple subextensions of purely transcendental field extensions. Appl. Algebra Engrg. Comm. Comput., 11(1):35–41, 2000.
[17] Guénael Renault. Computation of the splitting field of a dihedral polynomial. In ISSAC '06: Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, pages 290–297, New York, NY, USA, 2006. ACM Press.
[18] Blair K. Spearman, Kenneth S. Williams, and Qiduan Yang. The 2-power degree subfields of the splitting fields of polynomials with Frobenius Galois groups. Comm. Algebra, 31(10):4745–4763, 2003.
[19] Rainer Steinwandt and Jörn Müller-Quade. Freeness, linear disjointness, and implicitization—a classical approach. Beiträge Algebra Geom., 41(1):57–66, 2000.

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