Israel Journal of Mathematics

, Volume 82, Issue 1–3, pp 405–427

Braid group action via GLn(q) and Un(q), and Galois realizations

  • Helmut Völklein
Article

Abstract

We determine the braid group action on generating systems of a group that is the semi-direct product of a finite vector space with a group of scalars. This leads to Galois realizations of certain groups GLn(q) and PUn(q).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [MM]
    G. Malle and B.H. Matzat,Realisierung von Gruppen PSL 2(Fp)als Galoisgruppen über Q, Math. Annalen272 (1985), 549–565.MATHCrossRefMathSciNetGoogle Scholar
  2. [McL]
    J. McLaughlin,Some groups generated by transvections, Arch. Math.18 (1967), 364–368.MATHCrossRefMathSciNetGoogle Scholar
  3. [Mi]
    M.H. Mitchell,Determination of the finite quaternary linear groups, Trans. Am. Math. Soc.14 (1913), 123–142.CrossRefGoogle Scholar
  4. [V1]
    H. Völklein,GL n(q)as Galois group over the rationals, Math. Annalen293 (1992), 163–176.MATHCrossRefGoogle Scholar
  5. [V2]
    H. Völklein,Braid group action, embedding problems and the groups PGLn(q), PUn(q 2), preprint.Google Scholar
  6. [Wa]
    A. Wagner,Collineation groups generated by homologies of order greater than 2, Geom. Ded.7 (1978), 387–398.MATHGoogle Scholar

Copyright information

© Hebrew University 1993

Authors and Affiliations

  • Helmut Völklein
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Universität ErlangenGermany

Personalised recommendations