Siberian Mathematical Journal

, Volume 46, Issue 2, pp 246–253 | Cite as

On recognition of all finite nonabelian simple groups with orders having prime divisors at most 13

  • A. V. Vasil’ev
Article

Abstract

The spectrum of a group is the set of its element orders. We say that the problem of recognition by spectrum is solved for a finite group if we know the number of pairwise nonisomorphic finite groups with the same spectrum as the group under study. In this article the problem of recognition by spectrum is completely solved for every finite nonabelian simple group with orders having prime divisors at most 13.

Keywords

recognition by spectrum finite simple group group of Lie type 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mazurov V. D., “The set of orders of elements in a finite group,” Algebra and Logic, 33, No.1, 49–56 (1994).Google Scholar
  2. 2.
    Mazurov V. D., “Recognition of finite groups by a set of orders of their elements,” Algebra and Logic, 37, No.6, 371–379 (1998).Google Scholar
  3. 3.
    Shi W., “A characteristic property of PSL 2(7),” J. Austral. Math. Soc. Ser. A, 36, No.3, 354–356 (1984).Google Scholar
  4. 4.
    Shi W., “A characteristic property of A 5,” J. Southwest-China Teach. Univ., 3, 11–14 (1986).Google Scholar
  5. 5.
    Shi W., “A characteristic property of J 1 and PSL 2(2n),” Adv. Math., 16, 397–401 (1987).Google Scholar
  6. 6.
    Brandl R. and Shi W., “The characterization of PSL(2,q) by its element orders, ” J. Algebra, 163, No.1, 109–114 (1994).Google Scholar
  7. 7.
    Mazurov V. D., “Characterizations of groups by arithmetic properties,” Algebra Colloq., 11, No.1, 129–140 (2004).Google Scholar
  8. 8.
    Williams J. S., “Prime graph components of finite groups,” J. Algebra, 69, No.2, 487–513 (1981).Google Scholar
  9. 9.
    Kondrat’ev A. S., “On prime graph components for finite simple groups,” Mat. Sb., 180, No.6, 787–797 (1989).Google Scholar
  10. 10.
    Kondrat’ev A. S. and Mazurov V. D., “Recognition of alternating groups of prime degree from their element orders,” Siberian. Math. J., 41, No.2, 294–302 (2000).Google Scholar
  11. 11.
    Mazurov V. D., “Characterizations of finite groups by sets of all orders of the elements,” Algebra and Logic, 36, No.1, 23–32 (1997).Google Scholar
  12. 12.
    Conway J. H., Curtis R. T., Norton S. P., Parker R. A., and Wilson R. A., Atlas of Finite Groups, Clarendon Press, Oxford (1985).Google Scholar
  13. 13.
    Aleeva M. R., “On finite simple groups with the set of element orders as in a Frobenius group or a double Frobenius group,” Math. Notes, 73, No.3, 299–313 (2003).Google Scholar
  14. 14.
    Zavarnitsin A. V., Element Orders in Coverings of the Groups L n(q) and Recognition of the Alternating Group A 16 [in Russian], NIIDMI, Novosibirsk (2000).Google Scholar
  15. 15.
    Jansen C., Lux K., Parker R. A., and Wilson R. A., An Atlas of Brauer Characters, Clarendon Press, Oxford (1995).Google Scholar
  16. 16.
    The GAP Group, GAP—Groups, Algorithms, and Programming. Version 4.4. 2004 (http:// www.gap-system.org).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. V. Vasil’ev
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

Personalised recommendations