Advertisement

Siberian Mathematical Journal

, Volume 49, Issue 2, pp 353–361 | Cite as

The D π-property of linear and unitary groups

  • D. O. RevinEmail author
Article

Abstract

Given an arbitrary set π of primes, we complete the description of the finite linear and unitary groups having the D π-property.

Keywords

Hall π-subgroup Dπ-group projective special linear group projective special unitary group radical r-subgroup r-superlocal 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hall P., “Theorems like Sylow’s,” Proc. London Math. Soc., 6, No. 3, 286–304 (1956).zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Revin D. O. and Vdovin E. P., “Hall subgroups of finite groups,” in: Ischia Group Theory 2004: Proc. of a Conf. in Honour of Marcel Herzog. Contemp. Math., 2006, 402, pp. 229–265.MathSciNetGoogle Scholar
  3. 3.
    Thompson J. G., “Hall subgroups of the symmetric groups,” J. Combin. Theory Ser. A, 1, No. 2, 271–279 (1966).zbMATHCrossRefGoogle Scholar
  4. 4.
    Gross F., “On a conjecture of Philip Hall,” Proc. London Math. Soc. Ser. III, 52, No. 3, 464–494 (1986).zbMATHCrossRefGoogle Scholar
  5. 5.
    Revin D. O., “The D π-property in a class of finite groups,” Algebra and Logic, 41, No. 3, 187–206 (2002).CrossRefMathSciNetGoogle Scholar
  6. 6.
    Vdovin E. P. and Revin D. O., “Hall’s subgroups of odd order in finite groups,” Algebra and Logic, 41, No. 1, 8–29 (2002).CrossRefMathSciNetGoogle Scholar
  7. 7.
    Revin D. O., “The D π-property of finite groups in the case 2 ∉ π,” Proc. Steklov Inst. Math., Suppl. 1, 164–180 (2007).Google Scholar
  8. 8.
    Carter R. W., Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, Wiley & Sons, New York (1985).zbMATHGoogle Scholar
  9. 9.
    Humphreys J. E., Linear Algebraic Groups, Springer-Verlag, New York (1972).Google Scholar
  10. 10.
    Kondrat’ev V. A., “Subgroups of finite Chevalley groups,” Russian Math. Surveys, 41, No. 1, 65–118 (1986).zbMATHCrossRefGoogle Scholar
  11. 11.
    Kleidman P. B. and Liebeck M., The Subgroup Structure of the Finite Classical Groups, Cambridge Univ. Press, Cambridge (1990).zbMATHGoogle Scholar
  12. 12.
    Wielandt H., “Zum Satz von Sylow,” Math. Z., Bd 60, No. 4, 407–408 (1954).zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Mazurov V. D. and Revin D. O., “On the Hall D π-property for finite groups,” Siberian. Math. J., 38, No. 1, 106–113 (1997).zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Gorenstein D., Finite Simple Groups. An Introduction to Their Classification, Plenum, New York (1982).zbMATHGoogle Scholar
  15. 15.
    An J., “2-Weights for general linear groups,” J. Algebra, 149, No. 2, 500–527 (1992).zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    An J., “2-Weights for unitary groups,” Trans. Amer. Math. Soc., 339, No. 1, 251–278 (1993).zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Revin D. O., “Superlocals in symmetric and alternating groups,” Algebra and Logic, 42, No. 3, 192–206 (2003).CrossRefMathSciNetGoogle Scholar
  18. 18.
    Glauberman G., Factorization in Local Subgroups of Finite Groups, Amer. Math. Soc., Providence, RI (1976) (Conf. Ser. Math.; 33).Google Scholar
  19. 19.
    Borel A. and de Siebental J., “Les-sous-groupes fermés de rang maximum des groupes de Lie clos,” Comment. Math. Helv., 23, No. 3, 200–221 (1949).zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Dynkin E. B., “Semisimple subalgebras of semisimple Lie algebras,” Mat. Sb., 30, No. 2, 349–462 (1952).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

Personalised recommendations