Skip to main content
SpringerLink
Log in

Products of conjugacy classes in Chevalley groups II. Covering and generation

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

Abstract

In this paper we establish a relationship between generating numbers and covering numbers of conjugacy classes in Chevalley groups over algebraically closed fields.

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

  • [Bo] A. Borel,Linear Algebraic Groups, Springer-Verlag, Berlin, 1991.

    MATH  Google Scholar 

  • [B] N. Bourbaki,Groupes et algèbres de Lie IV, V, VI, Hermann, Paris, 1968.

    Google Scholar 

  • [C1] R. W. Carter,Simple Groups of Lie Type, John Wiley & Sons, London, 1989.

    MATH  Google Scholar 

  • [C2] R. W. Carter,Finite Groups of Lie Type, John Wiley & Sons, Chichester, 1993.

    Google Scholar 

  • [G] N. Gordeev,Products of conjugacy classes in algebraic groups I, II, Journal of Algebra173 (1995), 715–744, 745–779.

    Article  MATH  MathSciNet  Google Scholar 

  • [GS] N. Gordeev and J. Saxl,Products of conjugacy classes in Chevalley groups I. Extended covering numbers, Israel Journal of Mathematics, this volume.

  • [Gu] R. M. Guralnick,Some applications of subgroup structure to probabilistic generation and covers of curves, inAlgebraic groups and their representations (R. W. Carter and J. Saxl, eds.), Kluwer Academic Publishers, Dodrecht, Boston, London, 1998, pp. 301–320.

    Google Scholar 

  • [GK] R. M. Guralnick and W. M. Kantor,Probabilistic generation of finite simple groups, Journal of Algebra234 (2000), 743–792.

    Article  MATH  MathSciNet  Google Scholar 

  • [LS] M. Liebeck and A. Shalev,Diameters of finite simple groups: sharp bounds and applications, Annals of Mathematics154 (2001), 383–406.

    Article  MATH  MathSciNet  Google Scholar 

  • [St1] R. Steinberg,Lectures on Chevalley Groups, Yale University, 1967.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Russian State Pedagogical University, Moijka 48, 191-186, Sankt Petersburg, Russia

    Nikolai Gordeev

  2. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, CB3 0WB, Cambridge, England

    Jan Saxl

Authors
  1. Nikolai Gordeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Saxl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolai Gordeev.

Additional information

The authors gratefully acknowledge EPSRC grant GR58542. The first author acknowledges further a grant SFB 343 “Diskrete Strukturen in der Mathematik”. The second author thanks the Institute for Advanced Studies at The Hebrew University for its hospitality.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gordeev, N., Saxl, J. Products of conjugacy classes in Chevalley groups II. Covering and generation. Isr. J. Math. 130, 249–258 (2002). https://doi.org/10.1007/BF02764078

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02764078

Keywords

Search

Navigation