Skip to main content
SpringerLink
Log in

Residual properties of free groups, III

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

Abstract

In this paper we want to prove the following theorem: Letx be an infinite set of non-abelian finite simple groups. Then the free groupF 2 on 2 generators is residuallyx. This answers a question first posed by W. Magnus and later by A. Lubotzky [9], Yu. Gorchakov and V. Levchuk [4].

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. R. W. Carter,Simple Groups of Lie-type, Wiley, New York, 1972.

    MATH  Google Scholar 

  2. R. W. Carter,Conjugacy classes in the Weyl group, Comp. Math.25 (1972), 1–59.

    MATH  Google Scholar 

  3. R. W. Carter,Finite Groups of Lie-Type: Conjugacy Classes and Complex Characters, Wiley, New York, 1985.

    MATH  Google Scholar 

  4. Yu. M. Gorchakov and V. M. Levchuk,On approximation of free groups, alg. i Log.9, No. 4 (1970), 415–421.

    MATH  Google Scholar 

  5. R. Hartshorne,Algebraic Geometry, Springer, New York, 1977.

    MATH  Google Scholar 

  6. R. Katz and W. Magnus, Residual properties of free groups, Comm. Pure Appl. Math.22 (1969), 1–13.

    Article  MATH  MathSciNet  Google Scholar 

  7. V. M. Levchuk,A property of Suzuki groups, Alg. i Log.9, No. 4 (1970), 551–557.

    MathSciNet  Google Scholar 

  8. V. M. Levchuk and Y. N. Nuzhin,Structure of Ree groups, Alg. i. Log.24 No. 1 (1985), 26–41.

    MathSciNet  Google Scholar 

  9. A. Lubotzky,On a Problem of Magnus, Proc. Am. Math. Soc.98, No. 4 (1986), 583–585.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. C. Lyndon and J. L. Ullman,Pairs of real 2 by 2 matrices that generate free products, Mich. Math. J.15 (1968), 161–166.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Malle,The maximal subgroups of 2 F 4(q 2), J. Algebra, to appear.

  12. C. R. Matthews, L. N. Vaserstein and B. Weisfeiler,Congruence properties of Zariski-dense subgroups, Proc. London Math. Soc.48 (1984), 514–532.

    Article  MATH  MathSciNet  Google Scholar 

  13. D. Mumford,Algebraic Geometry, 1. Complex Projective Varieties, Springer, Berlin, 1976.

    Google Scholar 

  14. A. Peluso,A residual property of free groups, Comm. Pure Appl. Math.19 (1967), 435–437.

    Article  MathSciNet  Google Scholar 

  15. S. Pride,Residual properties of free groups, Pacific J. Math.43 (1972), 725–733.

    MATH  MathSciNet  Google Scholar 

  16. R. Steinberg,Representations of algebraic groups, Nagoya Math. J.22 (1963), 33–56.

    MATH  MathSciNet  Google Scholar 

  17. Th. Weigel,Residual Properties of Free Groups, Ph.D. Thesis, Freiburg, 1989.

  18. Th. Weigel,Residual properties of free groups, J. Algebra, to appear.

  19. Th. Weigel,Residual properties of free groups, II, Commun. Algebra, to appear.

  20. Th. Weigel,Generation of exceptional groups, Geom. Dedicata41 (1992), 63–87.

    Article  MATH  MathSciNet  Google Scholar 

  21. B. Weisfeiler,Strong approximation for Zariski-dense subgroups of semisimple algebraic groups, Ann. Math. (2)120 (1984), 271–315.

    Article  MathSciNet  Google Scholar 

  22. J. S. Wilson,A residual property of free groups, J. Algebra138 (1991), 36–47.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität Freiberg, Alberstr. 23b, D-7800, Freiberg, Germany

    T. S. Weigel

Authors
  1. T. S. Weigel
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weigel, T.S. Residual properties of free groups, III. Israel J. Math. 77, 65–81 (1992). https://doi.org/10.1007/BF02808011

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02808011

Keywords

Search

Navigation