Advertisement

Israel Journal of Mathematics

, Volume 31, Issue 1, pp 91–96 | Cite as

Frobenius Galois groups over quadratic fields

  • Jack Sonn
Article

Abstract

There exists a quadratic fieldQ(√D) over which every Frobenius group is realizable as a Galois group.

Keywords

Galois Group Number Field Semidirect Product Galois Extension Frobenius Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Dieudonné, On the automorphisms of the classical groups, Mem. Amer. Math. Soc.2 (1951), 1–95.Google Scholar
  2. 2.
    B. Huppert,Endliche Gruppen I, Springer-Verlag, Berlin, 1967.MATHGoogle Scholar
  3. 3.
    S. Lang,Algebraic Number Theory, Addison-Wesley, New York, 1970.MATHGoogle Scholar
  4. 4.
    J. Neukirch,Über das Einbettungsproblem der algebraischen Zahlentheorie, Invent. Math.21 (1973), 59–116.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    D. Passman,Permutation Groups, Benjamin, New York, 1968.MATHGoogle Scholar
  6. 6.
    A. Scholz,Über die Bildung algebraischer Zahlkörper mit auflösbarer Galoissche Gruppe, Math. Z.30 (1929), 332–356.CrossRefMathSciNetGoogle Scholar
  7. 7.
    J. Schur,Untersuchungen über die Darstellung endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math.132 (1907), 85–137.Google Scholar
  8. 8.
    W. R. Scott,Group Theory, Prentice-Hall, New Jersey, 1964.MATHGoogle Scholar
  9. 9.
    I. R. Shafarevich,On the problem of imbedding fields, Transl. Amer. Math. Soc., Ser. 2,4 (1956), 151–183.Google Scholar
  10. 10.
    I. R. Shafarevich,Construction of fields of algebraic numbers with given solvable Galois group, Transl. Amer. Math. Soc., Ser. 2,4 (1956), 185–237.Google Scholar
  11. 11.
    J. Thompson,Finite groups with fixed point free automorphisms of prime order, Proc. Nat. Acad. Sci. U.S.A.45 (1959), 578–581.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    K. Uchida,Unramified extensions of quadratic number fields, II, Tôhoku Math. J.22 (1970), 220–224.MATHMathSciNetGoogle Scholar
  13. 13.
    Y. Yamamoto,On unramified Galois extensions of quadratic number fields, Osaka J. Math.7 (1970), 57–76.MATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1978

Authors and Affiliations

  • Jack Sonn
    • 1
  1. 1.Faculty of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

Personalised recommendations