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2011 | 9 | 2 | 403-419
Tytuł artykułu

On Galois cohomology and realizability of 2-groups as Galois groups

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
In this paper we develop some new theoretical criteria for the realizability of p-groups as Galois groups over arbitrary fields. We provide necessary and sufficient conditions for the realizability of 14 of the 22 non-abelian 2-groups having a cyclic subgroup of index 4 that are not direct products of groups.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
2
Strony
403-419
Opis fizyczny
Daty
wydano
2011-04-01
online
2011-02-18
Twórcy
Bibliografia
  • [1] Bechtell H., The Theory of Groups, Addison-Wesley, Reading-London-Don Mills, 1971
  • [2] Fröhlich A., Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants, J. Reine Angew. Math., 1985, 360, 84–123
  • [3] Grundman H.G., Smith T.L., Realizability and automatic realizability of Galois groups of order 32, Cent. Eur. J. Math., 2010, 8(2), 244–260 http://dx.doi.org/10.2478/s11533-009-0072-x
  • [4] Grundman H.G., Smith T.L., Galois realizability of groups of order 64, Cent. Eur. J. Math., 2010, 8(5), 846–854 http://dx.doi.org/10.2478/s11533-010-0052-1
  • [5] Ishkhanov V.V., Lur’e B.B., Faddeev D.K., The Embedding Problem in Galois Theory, Transl. Math. Monogr., 165, American Mathematical Society, Providence, 1997
  • [6] Jacobson N., Basic Algebra II, 2nd ed., W.H. Freeman and Company, New York, 1989
  • [7] Kiming I., Explicit classifications of some 2-extensions of a field of characteristic different from 2, Canad. J. Math., 1990, 42(5), 825–855 http://dx.doi.org/10.4153/CJM-1990-043-6
  • [8] Ledet A., On 2-groups as Galois groups, Canad. J. Math., 1995, 47(6), 1253–1273 http://dx.doi.org/10.4153/CJM-1995-064-3
  • [9] Ledet A., Embedding problems with cyclic kernel of order 4, Israel J. Math., 1998, 106(1), 109–131 http://dx.doi.org/10.1007/BF02773463
  • [10] Ledet A., Brauer Type Embedding Problems, Fields Inst. Monogr., 21, American Mathematical Society, Providence, 2005
  • [11] Michailov I.M., Embedding obstructions for the dihedral, semidihedral, and quaternion 2-groups, J. Algebra, 2001, 245(1), 355–369 http://dx.doi.org/10.1006/jabr.2001.8926
  • [12] Michailov I.M., Embedding obstructions for the cyclic and modular 2-groups, Math. Balkanica (N.S.), 2007, 21(1–2), 31–50
  • [13] Michailov I.M., Four non-abelian groups of order p 4 as Galois groups, J. Algebra, 2007, 307(1), 287–299 http://dx.doi.org/10.1016/j.jalgebra.2006.05.021
  • [14] Michailov I.M., Groups of order 32 as Galois groups, Serdica Math. J., 2007, 33(1), 1–34
  • [15] Michailov I.M., Induced orthogonal representations of Galois groups, J. Algebra, 2009, 322(10), 3713–3732 http://dx.doi.org/10.1016/j.jalgebra.2009.07.035
  • [16] Michailov I.M., Ziapkov N.P., Embedding obstructions for the generalized quaternion group, J. Algebra, 2000, 226(1), 375–389 http://dx.doi.org/10.1006/jabr.1999.8190
  • [17] Ninomiya Y., Finite p-groups with cyclic subgroups of index p 2, Math. J. Okayama Univ., 1994, 36, 1–21
  • [18] Riehm C., The corestriction of algebraic structures, Invent. Math., 1970, 11(1), 73–98 http://dx.doi.org/10.1007/BF01389807
  • [19] Scharlau W., Quadratic and Hermitian Forms, Grundlehren Math.Wiss., 270, Springer, Berlin, 1985
  • [20] Serre J.-P., Cohomologie Galoisienne, Lecture Notes in Math., 5, Springer, Berlin-Heidelberg-New York, 1964
  • [21] Swallow J.R., Thiem F.N., Quadratic corestriction, C 2-embedding problems, and explicit construction, Comm. Algebra, 2002, 30(7), 3227–3258 http://dx.doi.org/10.1081/AGB-120004485
  • [22] Tignol J.-P., On the corestriction of central simple algebras, Math. Z., 1987, 194(2), 267–274 http://dx.doi.org/10.1007/BF01161974
  • [23] The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.10, 2007, http://www.gap-system.org
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0004-4
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