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Israel Journal of Mathematics

, Volume 130, Issue 1, pp 249–258 | Cite as

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

  • Nikolai Gordeev
  • Jan Saxl
Article

Abstract

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

Keywords

Conjugacy Class Algebraic Group Maximal Torus Chevalley Group Finite Simple Group 
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References

  1. [Bo] A. Borel,Linear Algebraic Groups, Springer-Verlag, Berlin, 1991.MATHGoogle Scholar
  2. [B] N. Bourbaki,Groupes et algèbres de Lie IV, V, VI, Hermann, Paris, 1968.Google Scholar
  3. [C1] R. W. Carter,Simple Groups of Lie Type, John Wiley & Sons, London, 1989.MATHGoogle Scholar
  4. [C2] R. W. Carter,Finite Groups of Lie Type, John Wiley & Sons, Chichester, 1993.Google Scholar
  5. [G] N. Gordeev,Products of conjugacy classes in algebraic groups I, II, Journal of Algebra173 (1995), 715–744, 745–779.MATHCrossRefMathSciNetGoogle Scholar
  6. [GS] N. Gordeev and J. Saxl,Products of conjugacy classes in Chevalley groups I. Extended covering numbers, Israel Journal of Mathematics, this volume.Google Scholar
  7. [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
  8. [GK] R. M. Guralnick and W. M. Kantor,Probabilistic generation of finite simple groups, Journal of Algebra234 (2000), 743–792.MATHCrossRefMathSciNetGoogle Scholar
  9. [LS] M. Liebeck and A. Shalev,Diameters of finite simple groups: sharp bounds and applications, Annals of Mathematics154 (2001), 383–406.MATHCrossRefMathSciNetGoogle Scholar
  10. [St1] R. Steinberg,Lectures on Chevalley Groups, Yale University, 1967.Google Scholar

Copyright information

© Hebrew University 2002

Authors and Affiliations

  1. 1.Department of MathematicsRussian State Pedagogical UniversitySankt PetersburgRussia
  2. 2.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeEngland

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