PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1997 | 82 | 2 | 129-145
Tytuł artykułu

On double covers of the generalized alternating group $ℤ_d ≀ 𝔄_m$ as Galois groups over algebraic number fields

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let $ℤ_d ≀ 𝔄}_m$ be the generalized alternating group. We prove that all double covers of $ℤ_d ≀ 𝔄}_m$ occur as Galois groups over any algebraic number field. We further realize some of these double covers as the Galois groups of regular extensions of ℚ(T). If d is odd and m >7, then every central extension of $ℤ_d ≀ 𝔄}_m$ occurs as the Galois group of a regular extension of ℚ(T). We further improve some of our earlier results concerning double covers of the generalized symmetric group $ℤ_d ≀ 𝔖_m$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
82
Numer
2
Strony
129-145
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-06-08
Twórcy
  • Fb Mathematik, Universität-Gesamthochschule Paderborn, D-33095 Paderborn, Germany
Bibliografia
  • [1] K. S. Brown, Cohomology of Groups, Grad. Texts in Math. 87, Springer, New York, 1982.
  • [2] M. Epkenhans, On the Galois group of $f(X^d)$, Comm. Algebra, to appear.
  • [3] M. Epkenhans, Trace forms of trinomials, J. Algebra 155 (1993), 211-220.
  • [4] M. Epkenhans, On double covers of the generalized symmetric group $ℤ_d ≀ 𝔖_m$ as Galois groups over algebraic number fields K with $μ_d ⊂ K$, J. Algebra 163 (1994), 404-423.
  • [5] B. Huppert, Endliche Gruppen I, Grundlehren Math. Wiss. 137, Springer, Berlin, 1967.
  • [6] M. Ikeda, Zur Existenz eigentlicher galoisscher Körper beim Einbettungsproblem für galoissche Algebren, Abh. Math. Sem. Univ. Hamburg 24 (1960), 126-131.
  • [7] G. Karpilovsky, The Schur Multiplier, London Math. Soc. Monographs (N.S.), Clarendon Press, London, 1987.
  • [8] D. Kotlar, M. Schacher and J. Sonn, Central extension of symmetric groups as Galois groups, J. Algebra 124 (1989), 183-198.
  • [9] S. Lang, Introduction to Algebraic Geometry, Addison-Wesley, 1972.
  • [10] B. H. Matzat, Konstruktive Galoistheorie, Lecture Notes in Math. 1284, Springer, Berlin, 1987.
  • [11] J. F. Mestre, Extensions régulières de ℚ(T) de groupe de Galois $Ã_n$, J. Algebra 131 (1990), 483-495.
  • [12] O. T. O'Meara, Introduction to Quadratic Forms, Springer, Berlin, 1963.
  • [13] M. Schacher and J. Sonn, Double covers of the symmetric groups as Galois groups over number fields, J. Algebra 116 (1988), 243-250.
  • [14] J. P. Serre, Corps Locaux, Hermann, Paris, 1968.
  • [15] J. P. Serre, L'invariant de Witt de la forme $Tr(x^2)$, Comment. Math. Helv. 59 (1984), 651-676.
  • [16] J. P. Serre, Topics in Galois Theory, 1, Res. Notes in Math. 1, Jones and Bartlett, Boston, 1992.
  • [17] J. Sonn, Central extensions of $S_n$ as Galois groups via trinomials, J. Algebra 125 (1989), 320-330.
  • [18] J. Sonn, Central extensions of S_n as Galois groups of regular extensions of ℚ(T), J. Algebra 140 (1991), 355-359.
  • [19] N. Vila, On central extensions of $A_n$ as Galois group over ℚ, Arch. Math. (Basel) 44 (1985), 424-437.
  • [20] N. Vila, On stem extensions of $S_n$ as Galois group over number fields, J. Algebra 116 (1988), 251-260.
  • [21] H. Völklein, Central extensions as Galois groups, J. Algebra 146 (1992), 144-152.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav82i2p129bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.