Journal of Mathematical Sciences

, Volume 130, Issue 3, pp 4768–4773 | Cite as

Towards the Hurwitz Generation of Gsc(E6, q)

  • N. S. Semenov
Article

Abstract

The paper is devoted to the problem concerning the Hurwitz generation of the group Gsc(E6, q). All possibilities for Hurwitz generators, except for just one, are excluded. Bibliography: 25 titles.

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REFERENCES

  1. 1.
    N. Bourbaki, Lie Groups and Algebras [Russian translation], Mir, Moscow (1972).Google Scholar
  2. 2.
    R. Steinberg, Lectures on Chevalley Groups, Yale University (1975).Google Scholar
  3. 3.
    M. Conder, “Generators for alternating and symmetric groups,” J. London Math. Soc., (2), 22, No.1, 75–86 (1980).Google Scholar
  4. 4.
    M. Conder, “Hurwitz groups: a brief survey,” Bull. Amer. Math. Soc., 23, No.2, 359–370 (1990).Google Scholar
  5. 5.
    M. Conder, “Two element generation of the finite reflection groups,” Quart. J. Math. Oxford, Ser. (2), 46, No.181, 95–106 (1995).Google Scholar
  6. 6.
    M. Conder, “Some results on quotients of triangle groups,” Bull. Austral. Math. Soc., 30, No.1, 73–90 (1984).Google Scholar
  7. 7.
    M. Conder, “More on generators for alternating and symmetric groups,” Quart. J. Math. Oxford. Ser. (2), 32, No.126, 137–163 (1981).Google Scholar
  8. 8.
    L. Di Martino and M. C. Tamburini, “2-generation of finite simple groups and some related topics,” in: Generators and Relations in Groups and Geometries, A. Barlotti et al., Kluwer Acad. Publ. (1991), pp. 195–233.Google Scholar
  9. 9.
    L. Di Martino, M. C. Tamburini, and A. E. Zalesskii, “On Hurwitz groups of low rank,” Comm. Algebra, 28, No.11, 5383–5404 (2000).Google Scholar
  10. 10.
    L. Di Martino and N. Vavilov, “(2, 3)-generation of SL(n, q). I. Cases n = 5, 6, 7,” Comm. Algebra, 22, No.4, 1321–1347 (1994).Google Scholar
  11. 11.
    L. Di Martino and N. Vavilov, “(2, 3)-generation of SL(n, q). II. Cases n ⩾ 8,” Comm. Algebra, 24, 487–515 (1996).Google Scholar
  12. 12.
    M. W. Liebeck and A. Shalev, “Classical groups, probabilistic methods, and the (2,3)-generation problem,” Ann. Math., 144, 77–125 (1996).Google Scholar
  13. 13.
    A. Lucchini, “(2, 3, k)-generated groups of large rank,” Arc. Math., 73, No.4, 241–248 (1999).CrossRefGoogle Scholar
  14. 14.
    A. Lucchini and M. C. Tamburini, “Classical groups of large rank as Hurwitz groups,” J. Algebra, 219, 531–546 (1999).CrossRefGoogle Scholar
  15. 15.
    A. Lucchini, M. C. Tamburini, and J. S. Wilson, “Hurwitz groups of large rank,” J. London Math. Soc., (2), 61, No.1, 81–92 (2000).Google Scholar
  16. 16.
    F. Lubeck and G. Malle, “(2,3)-generation of exceptional groups,” Preprint, Univ. Heidelberg (1996).Google Scholar
  17. 17.
    G. Malle, “Hurwitz groups and G2,” Canad. Math. Bull., 33, No.3, 349–357 (1990).Google Scholar
  18. 18.
    G. Malle, “Small rank exceptional Hurwitz groups,” in: Groups of Lie Type and Their Geometries, Cambridge University Press (1995), pp. 173–183.Google Scholar
  19. 19.
    E. Plotkin, A. Semenov, and N. Vavilov, “Visual basic representations: an atlas,” Int. J. Algebra and Comput., 8, No.1, 61–95 (1998).CrossRefGoogle Scholar
  20. 20.
    L. L. Scott, “Matrices and cohomology,” Ann. Math., 105, 473–492 (1977).Google Scholar
  21. 21.
    M. C. Tamburini, J. S. Wilson, and N. Gavioli, “On the (2,3)-generation of some classical groups. I,” J. Algebra, 168, 353–370 (1994).CrossRefGoogle Scholar
  22. 22.
    M. C. Tamburini and J. S. Wilson, “On the (2,3)-generation of some classical groups. II,” J. Algebra, 176, 667–680 (1995).CrossRefGoogle Scholar
  23. 23.
    M. C. Tamburini and S. Vassallo, “(2, 3)-generazione di SL(4, q) in caratteristica dispari e problemi collegati,” Boll. Un. Math. Ital. to appear.Google Scholar
  24. 24.
    N. Vavilov, “Structure of Chevalley groups over commutative rings,” in: Proceedings of the Conference on Nonassociative Algebras and Related Topics (Hiroshima, 1990), World Scientific, London (1991), pp. 219–335.Google Scholar
  25. 25.
    N. Vavilov, “A third look at weight diagrams,” Rend. Sem. Math. Univ. Padova, 104, No.1, 201–250 (2000).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • N. S. Semenov
    • 1
  1. 1.Department of Mathematics, Statistics&Computing ScienceDalhousie UniversityCanada

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