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 (2001), no. 2, 608–635.[MR]
  2. Maximilian Albert and Annette Maier, Additive polynomials for finite groups of Lie type, preprint (2009), 59 pages.[arXiv]
  3. Bill Allombert, An efficient algorithm for the computation of Galois automorphisms, Math. Comp. 73 (2004), no. 245, 359–375 (electronic).[MR]
  4. Johan Bosman, A polynomial with Galois group SL2( F16), LMS J. Comput. Math. 10 (2007), 1461–1570 (electronic).[MR/arXiv]
  5. Nigel Boston, Reducing the Fontaine-Mazur conjecture to group theory, Progress in Galois theory, Dev. Math., vol. 12, Springer, New York, 2005, pp. 39–50.[MR]
  6. Nigel Boston and Charles Leedham-Green, Explicit computation of Galois p-groups unramified at p, J. Algebra 256 (2002), no. 2, 402–413.[MR]
  7. Nigel Boston and Harris Nover, Computing pro-p-Galois groups, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 1–10.[MR]
  8. Nigel Boston and David Perry, Maximal 2-extensions with restricted ramification, J. Algebra 232 (2000), no. 2, 664–672.[MR]
  9. 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), ACM, New York, 1997, pp. 78–84 (electronic).[MR]
  10. Lassina Dembélé, A non-solvable Galois extension of Q ramified at 2 only, C. R. Math. Acad. Sci. Paris 347 (2009), no. 3-4, 111–116.[MR/doi]
  11. Michael Dettweiler, Galois realizations of classical groups and the middle convolution, preprint (2006), 94 pages.[arXiv]
  12. Pilar Fernandez-Ferreiros and M. Angeles Gomez-Molleda, Deciding the nilpotency of the Galois group by computing elements in the centre, Math. Comp. 73 (2004), no. 248, 2043–2060 (electronic).[MR]
  13. Louis Granboulan, Construction d'une extension régulière de Q(T) de groupe de Galois M24, Experiment. Math. 5 (1996), no. 1, 3–14.[MR]
  14. Farshid Hajir, On the Galois group of generalized Laguerre polynomials, J. Théor. Nombres Bordeaux 17 (2005), no. 2, 517–525.[MR]
  15. Farshid Hajir, Tame pro-p Galois groups: A survey of recent work, Arithmetic, Geometry and Coding Theory (AGCT 2003), Sémin. Congr., vol. 11, Soc. Math. France, Paris, 2005, pp. 111–124.[MR]
  16. Emmanuel Hallouin, Study and computation of a Hurwitz space and totally real PSL2(F8)-extensions of Q, J. Algebra 292 (2005), no. 1, 259–281.[MR]
  17. 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, ACM, New York, 2001, pp. 175–182 (electronic).[MR]
  18. Florent Jouve, Emmanuel Kowalski, and David Zywina, An explicit integral polynomial whose splitting field has galois group W(E8), J. Théor. Nombres Bordeaux 20 (2008), no. 3, 761–782.[MR]
  19. Gregor Kemper and Gunter Malle, Invariant fields of finite irreducible reflection groups, Math. Ann. 315 (1999), no. 4, 569–586.[MR]
  20. Masanari Kida, Guénaël Renault, and Kazuhiro Yokoyama, Quintic polynomials of Hashimoto-Tsunogai, Brumer and Kummer, Int. J. Number Theory 5 (2009), no. 4, 555–571.[MR/doi]
  21. Jürgen Klüners and Gunter Malle, Explicit Galois realization of transitive groups of degree up to 15, J. Symbolic Comput. 30 (2000), no. 6, 675–716.[MR]
  22. Aristides Kontogeorgis, The group of automorphisms of cyclic extensions of rational function fields, J. Algebra 216 (1999), no. 2, 665–706.[MR]
  23. Jörn Müller-Quade and Rainer Steinwandt, Recognizing simple subextensions of purely transcendental field extensions, Appl. Algebra Engrg. Comm. Comput. 11 (2000), no. 1, 35–41.[MR]
  24. Renault Guénaél Renault, Computation of the splitting field of a dihedral polynomial, in ISSAC '06: Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ACM Press, New York, NY, USA, 2006, pp. 290–297.[doi]
  25. Núria Vila Sara Arias-de-Reyna, Tame Galois realizations of GSp4(Fl) over Q, preprint (2009), 29 pages.[arXiv]
  26. Romyar T. Sharifi, On Galois groups of unramified pro-p extensions, Math. Ann. 342 (2008), no. 2, 297–308.[MR]
  27. 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 (2003), no. 10, 4745–4763.[MR]
  28. Rainer Steinwandt and Jörn Müller-Quade, Freeness, linear disjointness, and implicitization—a classical approach, Beiträge Algebra Geom. 41 (2000), no. 1, 57–66.[MR]