Israel Journal of Mathematics

, Volume 82, Issue 1–3, pp 141–156 | Cite as

TheK-admissibility of 2A 6 and 2A 7

  • Walter Feit


LetK be a field and letG be a finite group.G isK-admissible if there exists a Galois extensionL ofK withG=Gal(L/K) such thatL is a maximal subfield of a centralK-division algebra. This paper contains a characterization of those number fields which areQ 16-admissible. This is the same class of number fields which are 2A 6=SL(2, 9) and 2A 7 admissible.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. Fein and M. Schacher,Q-admissibility questions for alternating groups, J. Algebra142 (1991), 360–382.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    W. Feit,The Q-admissibility of 2A 6 and 2A 7, to appear.Google Scholar
  3. [3]
    P. Feit and W. Feit,The K-admissibility of SL(2,5), Geometriae Dedicata36 (1990), 1–13.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    J.-F. Mestre,Extensions reguliéres de Q(T)de groupe de Galois à n, J. Algebra131 (1990), 483–496.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    M. Schacher,Subfields of division rings, J. Algebra9 (1968), 451–477.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    M. Schacher and J. Sonn,K-Admissibility of A 6 and A 7, J. Algebra145 (1992), 333–338.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    J.-P. Serre,L’invariant de Witt de la forme Tr(x 2), Comment. Math. Helv.59 (1984), 651–676.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1993

Authors and Affiliations

  • Walter Feit
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Personalised recommendations