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2010 | 8 | 2 | 244-260
Tytuł artykułu

Realizability and automatic realizability of Galois groups of order 32

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article provides necessary and sufficient conditions for each group of order 32 to be realizable as a Galois group over an arbitrary field. These conditions, given in terms of the number of square classes of the field and the triviality of specific elements in related Brauer groups, are used to derive a variety of automatic realizability results.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
2
Strony
244-260
Opis fizyczny
Daty
wydano
2010-04-01
online
2010-04-14
Twórcy
autor
Bibliografia
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  • [3] The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.9, 2006, 〈http://www.gap-system.org〉
  • [4] Grundman H.G., Smith T.L., Automatic realizability of Galois groups of order 16, Proc. AMS, 1996, 124, 2631–2640 http://dx.doi.org/10.1090/S0002-9939-96-03345-X
  • [5] Grundman H.G., Smith T.L., Galois realizability of acentral C 4-extension of D 8, J. Alg., 2009, 322, 3492–3498 http://dx.doi.org/10.1016/j.jalgebra.2009.08.015
  • [6] Grundman H.G., Smith T.L., Swallow J. R., Groups of order 16 as Galois groups, Expo. Math., 1995, 13, 289–319
  • [7] Grundman H.G., Stewart G., Galois realizability of non-split group extensions of C 2 by (C 2)r × (C 4)s × (D 4)t, J. Algebra, 2004, 272, 425–434 http://dx.doi.org/10.1016/j.jalgebra.2003.09.017
  • [8] Hall M.Jr., Senior J.K., The Groups of Order 2n (n ≤ 6), Macmillian, New York, 1964
  • [9] Ishkhanov V.V., Lur’e B.B., Faddeev D.K., The Embedding Problem in Galois Theory, Translations of Mathematical Monographs, 165, American Mathematical Society, Providence, R.I., 1997
  • [10] Jensen C.U., On the representation of a group as a Galois group over an arbitrary field, In: De Koninck J.-M., Levesque C. (Eds.), Theoriedes Nombres - Number Theory, Walterde Gruyter, 1989, 441–458
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  • [12] Ledet A., On 2-groups as Galois groups, Canad. J. Math., 1995, 47, 1253–1273
  • [13] Ledet A., Embedding problems with cyclic kernel of order 4, Israel J. Math., 1998, 106, 109–131 http://dx.doi.org/10.1007/BF02773463
  • [14] Michailov I., Embedding obstructions for the cyclic and modular 2-groups, Math. Balkanica (N.S.), 2007, 21, 31–50
  • [15] Michailov I., Groups of order 32 as Galois groups, Serdica Math. J., 2007, 33, 1–34
  • [16] Smith T.L., Extra-special 2-groups of order 32 as Galois groups, Canad. J. Math., 1994, 46, 886–896
  • [17] Swallow J., Thiem N., Quadratic corestriction, C 2-embedding problems, and explicit construction, Comm. Algebra, 2002, 30, 3227–3258 http://dx.doi.org/10.1081/AGB-120004485
  • [18] Witt E., Konstruktion von Galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung p f, J. Reine Angew. Math., 1936, 174, 237–245 (in German)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0072-x
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