Skip to main content
SpringerLink
Log in

Braid group action via GL n (q) and U n (q), and Galois realizations

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

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 GL n (q) and PU n (q).

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

Similar content being viewed by others

References

  1. G. Malle and B.H. Matzat,Realisierung von Gruppen PSL 2(F p )als Galoisgruppen über Q, Math. Annalen272 (1985), 549–565.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. McLaughlin,Some groups generated by transvections, Arch. Math.18 (1967), 364–368.

    Article  MATH  MathSciNet  Google Scholar 

  3. M.H. Mitchell,Determination of the finite quaternary linear groups, Trans. Am. Math. Soc.14 (1913), 123–142.

    Article  Google Scholar 

  4. H. Völklein,GL n (q)as Galois group over the rationals, Math. Annalen293 (1992), 163–176.

    Article  MATH  Google Scholar 

  5. H. Völklein,Braid group action, embedding problems and the groups PGL n (q), PU n (q 2), preprint.

  6. A. Wagner,Collineation groups generated by homologies of order greater than 2, Geom. Ded.7 (1978), 387–398.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    Helmut Völklein

  2. Universität Erlangen, Germany

    Helmut Völklein

Authors
  1. Helmut Völklein
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Prof. J. G. Thompson

Partially supported by an NSA grant.

This work was done while the author was a fellow of the Institute for Advanced Studies in Jerusalem.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Völklein, H. Braid group action via GL n (q) and U n (q), and Galois realizations. Israel J. Math. 82, 405–427 (1993). https://doi.org/10.1007/BF02808122

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02808122

Keywords

Search

Navigation