Israel Journal of Mathematics

, Volume 82, Issue 1–3, pp 281–297

On extensions of the Baer-Suzuki Theorem



We find a necessary and sufficient condition for an element of prime order in a finite group to be in a normalp-subgroup. This generalizes the Baer-Suzuki Theorem. Our proof depends on a result about elements of prime order contained in a unique maximal subgroup containing a result of Wielandt. We discuss various consequences, linear and algebraic group versions of the result.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AL]
    J. Alperin and R. Lyons,Conjugacy classes of p-elements, J. Algebra19 (1971), 536–537.MATHCrossRefMathSciNetGoogle Scholar
  2. [Ar]
    O. D. Artemovich,Isolated elements of prime order in finite groups, Ukranian Math. J.40 (1988), 397–400.MATHMathSciNetGoogle Scholar
  3. [A1]
    M. Aschbacher,The 27-dimensional module for E 6,IV, J. Algebra131 (1990), 23–39.MATHCrossRefMathSciNetGoogle Scholar
  4. [A2]
    M. Aschbacher,Overgroups of Sylow subgroups in sporadic groups, Memoirs of the Amer. Math. Soc.60 (1986), No. 343.Google Scholar
  5. [B]
    A. Borel,Linear Algebraic Groups, 2nd Ed., Springer-Verlag, New York, 1991.MATHGoogle Scholar
  6. [F]
    W. Feit,The Representation Theory of Finite Groups, North-Holland Publishing Company, Amsterdam, 1982.MATHGoogle Scholar
  7. [G1]
    D. Gorenstein,Finite Groups, Harper & Row, New York, 1968.MATHGoogle Scholar
  8. [G2]
    D. Gorenstein,Finite Simple Groups — An Introduction to their Classification, Plenum Press, New York, 1982.MATHGoogle Scholar
  9. [Gr]
    F. Gross,Automorphisms which centralize a Sylow p-subgroup, J. Algebra77 (1982), 202–233.MATHCrossRefMathSciNetGoogle Scholar
  10. [H]
    J. Humphreys,Linear Algebric Groups, Springer-Verlag, New York, 1975.Google Scholar
  11. [S]
    G. Seitz,Generation of finite groups of Lie type, Trans. Amer. Math. Soc.271 (1982), 351–407.MATHCrossRefMathSciNetGoogle Scholar
  12. [St]
    R. Steinberg,Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc.,80, 1968.Google Scholar
  13. [Wa]
    H. N. Ward,On Ree’s series of simple groups, Trans. Amer. Math. Soc.121 (1966), 62–89.MATHCrossRefMathSciNetGoogle Scholar
  14. [W]
    H. Wielandt,Kriterien für Subnormalität in endlichen Gruppen, Math Z.138 (1974), 199–203.MATHCrossRefMathSciNetGoogle Scholar
  15. [X]
    Wen-Jun Xiao,Glauberman’s conjecture, Mazurov’s problem and Peng’s problem, Science in China Series A34 (1991), 1025–1031.MATHGoogle Scholar

Copyright information

© Hebrew University 1993

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Southern CalforniaLos AngelesUSA
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA

Personalised recommendations