PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 5 | 910-923
Tytuł artykułu

Galois realizability of groups of orders p 5 and p 6

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let p be an odd prime and k an arbitrary field of characteristic not p. We determine the obstructions for the realizability as Galois groups over k of all groups of orders p 5 and p 6 that have an abelian quotient obtained by factoring out central subgroups of order p or p 2. These obstructions are decomposed as products of p-cyclic algebras, provided that k contains certain roots of unity.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
5
Strony
910-923
Opis fizyczny
Daty
wydano
2013-05-01
online
2013-03-14
Twórcy
Bibliografia
  • [1] Albert A.A., Modern Higher Algebra, University of Chicago Press, Chicago, 1937
  • [2] Grundman H.G., Smith T.L., Galois realizability of a central C 4-extension of D 8, J. Algebra, 2009, 322(10), 3492–3498 http://dx.doi.org/10.1016/j.jalgebra.2009.08.015
  • [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, Amerecian Mathematical Society, Providence, 1997
  • [6] James R., The groups of order p 6 (p an odd prime), Math. Comp., 1980, 34(150), 613–637
  • [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., Brauer Type Embedding Problems, Fields Inst. Monogr., 21, American Mathematical Society, Providence, 2005
  • [10] Massy R., Construction de p-extensions galoisiennes d’un corps de caractéristique différente de p, J. Algebra, 1987, 109(2), 508–535 http://dx.doi.org/10.1016/0021-8693(87)90153-0
  • [11] Merkur’ev A.S., Suslin A.A., K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR Ser. Mat., 1982, 46(5), 1011–1046 (in Russian)
  • [12] Michailov I.M., Groups of order 32 as Galois groups, Serdica Math. J., 2007, 33(1), 1–34
  • [13] Michailov I.M., Embedding obstructions for the cyclic and modular 2-groups, Math. Balkanica (N.S.), 2007, 21(1–2), 31–50
  • [14] 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
  • [15] Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 2011, 403–419 http://dx.doi.org/10.2478/s11533-011-0004-4
  • [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] Michailov I.M., Ziapkov N.P., On realizability of p-groups as Galois groups, Serdica Math. J., 2011, 37(3), 173–210
  • [18] Pierce R.S., Associative Algebras, Grad. Texts in Math., 88, Springer, New York-Berlin, 1982
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0217-9
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.