Skip to main content
SpringerLink
Log in

Einige orthogonale und symplektische Gruppen als Galoisgruppen über ℚ

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literatur

  1. Belyi, G.V.: On Galois extensions of a maximal cyclotomic field. Math. USSR, Izv.14, 247–256 (1980)

    Google Scholar 

  2. Belyi, G.V.: On extensions of the maximal cyclotomic field having a given classical Galois group. J. Reine Angew. Math.341, 147–156 (1983)

    Google Scholar 

  3. Boyce, R.A.: Irreducible representations of finite groups of Lie type through block theory and special conjugacy classes. Pac. J. Math.102, 253–274 (1982)

    Google Scholar 

  4. Butler, G., McKay, J.: The transitive groups of degree up to 11. Commun. Algebra11, 863–911 (1983)

    Google Scholar 

  5. Carter, R.W.: Conjugacy classes in the Weyl group. Compos. Math.25, 1–59 (1972)

    Google Scholar 

  6. Carter, R.W.: Finite groups of Lie type: Conjugacy classes and complex characters. New York: Wiley 1985

    Google Scholar 

  7. Chang, B.: The conjugate classes of Chevalley groups of type (G 2). J. Algebra9, 190–211 (1968)

    Google Scholar 

  8. Chang, B., Ree, R.: The characters ofG 2(q). Symp. Math.XIII, 395–413 (1974)

    Google Scholar 

  9. Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of finite groups. Oxford: Clarendon 1985

    Google Scholar 

  10. Dentzer, R.: Projektive symplektische GruppenPSp 4(p) als Galoisgruppen. Arch. Math.53, 337–346 (1989)

    Google Scholar 

  11. Fischer, B.: Finite groups generated by 3-transpositions. Invent. Math.13, 232–246 (1971)

    Google Scholar 

  12. Häfner, F.: Einige orthogonale und symplektische Gruppen als Galoisgruppen über ℚ. Dissertation, Heidelberg 1991

  13. Hiß, G.: A converse to the Fong-Swan-Isaacs theorem. J. Algebra111, 279–290 (1987)

    Google Scholar 

  14. Hiß, G.: Zerlegungszahlen endlicher Gruppen vom Lie-Typ in nicht-definierender Charakteristik. Habilitationsschrift, Aachen 1990

  15. Kleidman, P.B.: The maximal subgroups of the Chevalley groupsG 2(q) withq odd, the Ree groups2 G 2(q), and their automorphism groups. J. Algebra117 30–71 (1988)

    Google Scholar 

  16. Kleidman, P.B.: Maximal subgroups of low dimensional classical groups. Erscheint in Longman Research Notes

  17. Malle, G.: Polynomials for primitive nonsolvable permutation groups of degreed≦15. J. Symb. Comput.4, 83–92 (1987)

    Google Scholar 

  18. Malle, G.: Polynomials with Galois groups Aut(M 22),M 22 andPSL 2(4)·2 over ℚ. Math. Comput.51 (184), 761–768 (1988)

    Google Scholar 

  19. Matzat, B.H.: Konstruktion von Zahl- und Funktionenkörpern mit vorgegebener Galoisgruppe. J. Reine Angew. Math.349, 179–220 (1984)

    Google Scholar 

  20. Matzat, B.H.: Konstruktive Galoistheorie. (Lect. Notes. Math., vol. 1284) Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  21. Matzat, B.H.: Frattini-Einbettungsprobleme über Hilbertkörpern. Manuscr. Math.70, 429–439 (1991)

    Google Scholar 

  22. Matzat, B.H.: Der Kenntnisstand in der konstruktiven Galoisschen Theorie. In: Michler, G.O., Ringel, C.M. (eds.) Representation theory of finite groups and finite-dimensional algebras. (Prog. Math., vol. 95, pp. 65–98) Basel: Birkhäuser 1991

    Google Scholar 

  23. McLaughlin, J.: Some subgroups of SL n (F 2). Ill. J. Math.13, 108–115 (1969)

    Google Scholar 

  24. Narkiewicz, W.: Elementary and analytic theory of algebraic numbers. Berlin Heidelberg New York: Springer 1989

    Google Scholar 

  25. Serre, J.-P.: Local fields. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  26. Serre, J.-P.: L'invariant de Witt de la formeTr(x 2). Comment. Math. Helv.59, 651–676 (1984)

    Google Scholar 

  27. Serre, J.-P.: Topics in Galois Theory. Erscheint bei Jones and Bartlett Publ., Boston

  28. Sims, C.C.: Computational methods in the study of permutation groups. In: Leech, J. (ed.) Computational problems in abstract algebra, pp. 169–183. Oxford: Pergamon 1970

    Google Scholar 

  29. Thompson, J.G.: Primitive roots and rigidity. In: Aschbacher, M. (ed.) Proceedings of the Rutgers group theory year, 1983–84, pp. 327–350. Cambridge University Press 1984

  30. Trinks, W.: On improving approximate results of Buchberger's algorithm by Newton's method. SIGSAM Bull.18, 7–11 (1984)

    Google Scholar 

  31. Wall, G.E.: On the conjugacy classes in the unitary, symplectic and orthogonal groups. J. Aust. Math. Soc.3, 1–62 (1963)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen der Universität Heidelberg, Im Neuenheimer Feld 368, W-6900, Heidelberg, Federal Republic of Germany

    Frank Häfner

Authors
  1. Frank Häfner
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Der Autor dankt der Deutschen Forschungsgemeinschaft für finanzielle Unterstützung

Rights and permissions

Reprints and permissions

About this article

Cite this article

Häfner, F. Einige orthogonale und symplektische Gruppen als Galoisgruppen über ℚ. Math. Ann. 292, 587–618 (1992). https://doi.org/10.1007/BF01444638

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444638

Search

Navigation