Skip to main content
Log in

(2,3)-generation of PSp(4, q), q = p n, p ≠ 2,3

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper we show that the symplectic group PSp(4, q), q = pn, p ≠ 2,3, is generated by an involution and an element of order 3.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Aschbacher, Finite Group Theory, Cambridge Studies in Advanced Mathematics, 10, 1986.

  2. M. Aschbacher, “On the maximal subgroups of the finite classical groups”, Invent Math., 76, 469–514, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Bertini, Introduzione alla geometria degli iperspazi, Enrico Sperri, Pisa, 1907.

    MATH  Google Scholar 

  4. E. Bertini, Complementi di geometria proiettiva, Zanichelli, Bologna, 1927.

    Google Scholar 

  5. J. Cohen, “On non-Hurwitz groups”, Glasgow Math. J., 22, 1–7, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Dieudonné, La géométrie des groupes classiques, Springer-Verlag, Berlin, 1955.

    MATH  Google Scholar 

  7. L. Di Martino and M. C. Tamburini. “2-generation of finite simple groups and some related topics”. In A. Barlotti et al., editors, Generators and Relations in Groups and Geometries, pages 195-233, Kluwer Academic Publishers, 1991.

  8. L. Di Martino and N. Vavilov, “(2,3)-generation of SL(n,q), I. Cases n = 5,6,7”, submitted.

  9. L. Di Martino and N. Vavilov, “(2,3)-generation of SL(n, q), II.”, in preparation.

  10. D. Garbe, “Über eine Klasse von arithmetisch definierbaren Normalteilern der Modulgruppe”, Math. Ann., 235, 195–215,1978.

    Article  MathSciNet  MATH  Google Scholar 

  11. P. Kleidman and M. Liebeck, The Subgroup Structure of the Finite Classical Groups, Cambridge University Press, 1990.

  12. H. Lüneburg, Translation Planes, Springer-Verlag, Berlin, 1980.

    Book  MATH  Google Scholar 

  13. H. H. Mitchell, “The subgroups of the quaternary abelian linear group”, Transaction of the American Mathematical Society, 15, 379–396, 1914.

    Article  MATH  Google Scholar 

  14. A. W. Macbeath, “Generators of linear fractional groups”, Proc. Symp. Pure Math., 12, 14–32, 1967.

    Article  Google Scholar 

  15. G. Malle, “Exceptional groups of Lie type as Galois groups”, J. reine angew. Math., 392, 70–109,1988.

    MathSciNet  MATH  Google Scholar 

  16. G. Malle, “Hurwitz groups and G2”, Canad. Math. Bull, 33 n. 3., 349–357,1990.

    Article  MathSciNet  MATH  Google Scholar 

  17. G. Malle, J. Saxl and T. Weigel, “Generation of classical groups”, to appear.

  18. J. G. Semple and G. T. Kneebone, Algebraic Projective Geometry, Oxford University Press, 1952.

  19. M. C. Tamburini, “Generation of certain simple groups by elements of small order”, Rend. 1st. Lomb. Sci., A121, 21–27, 1987.

    MathSciNet  Google Scholar 

  20. M. C. Tamburini and S. Vassallo, “(2,3)-generazione di S L(4, q) in caratteristica dispari e problemi collegati”, submitted.

  21. B. L. Van der Waerden, Gruppen von linearen Transformationen, Springer-Verlag, Berlin, 1935.

  22. A. J. Woldar, “On Hurwitz generation and genus action of sporadic groups”, Illinois Math. J., 33, 416–437, 1989.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The authors were supported by M.U.R.S.T. and C.N.R. (Italy)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cazzola, M., Di Martino, L. (2,3)-generation of PSp(4, q), q = p n, p ≠ 2,3. Results. Math. 23, 221–232 (1993). https://doi.org/10.1007/BF03322298

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322298

AMS 1991 Subject Classification

Keywords

Navigation