Skip to main content
Log in

On the finite groups whose Sylow 3-subgroup normalizes a Sylow 3′-subgroup

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We determine the possible composition factors of finite groups in which the index of the normalizer of a Sylow 3-subgroup is not divisible by a prime s > 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. Kondrat’ev A. S. and Guo Wenbin, “Finite groups in which the normalizers of Sylow 3-subgroups are of odd or primary index,” Siberian Math. J., 50, No. 2, 272–276 (2009).

    Article  MathSciNet  Google Scholar 

  2. Huppert B., Endliche Gruppen. I, Springer-Verlag, Berlin (1967).

    Book  MATH  Google Scholar 

  3. Gorenstein D. and Lyons R., The Local Structure of Finite Groups of Characteristic 2 Type, Amer. Math. Soc., Providence, RI (1983) (Mem. Amer. Math. Soc.; V. 42, No. 276).

    Google Scholar 

  4. Gorenstein D., Lyons R., and Solomon R., The Classification of the Finite Simple Groups, Amer. Math. Soc., Providence, RI (1998) (Math. Surveys Monogr.; V. 40(3)).

    MATH  Google Scholar 

  5. Kondrat’ev A. S., “Subgroups of finite Chevalley groups,” Russian Math. Surveys, 41, No. 1, 65–118 (1986).

    Article  MATH  Google Scholar 

  6. Gross F., “On a conjecture of Philip Hall,” Proc. London Math. Soc., 52, No. 3, 464–494 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  7. Vdovin E. P. and Revin D. O., “Theorems of Sylow type,” Uspekhi Mat. Nauk, 66, No. 5, 3–46 (2011).

    Article  MathSciNet  Google Scholar 

  8. Wielandt H., “Zum Satz von Sylow,” Math. Z., Bd 60, No. 4, 407–408 (1954).

    Article  MATH  MathSciNet  Google Scholar 

  9. Gross F., “Automorphisms which centralize a Sylow p-subgroup,” J. Algebra, 77, No. 1, 202–233 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  10. Seminar on Algebraic Groups [Russian translation], Eds.: Borel A.; Carter R.; Curtis C. W.; Iwahori N.; Springer T. A.; Steinberg R., Mir, Moscow (1973).

    MATH  Google Scholar 

  11. Liebeck M. and Saxl J., “On the orders of maximal subgroups of the finite exceptional groups of Lie type,” Proc. London Math. Soc., 55, No. 2, 299–330 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  12. Conway J. H., Curtis R. T., Norton S. P., Parker R. A., and Wilson R. A., Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, Clarendon Press, Oxford (1985).

    MATH  Google Scholar 

  13. Vdovin E. P. and Revin D. O., “Hall subgroups of odd order in finite groups,” Algebra and Logic, 41, No. 1, 8–29 (2002).

    Article  MathSciNet  Google Scholar 

  14. Syskin S. A., “Abstract properties of the simple sporadic groups,” Russian Math. Surveys, 35, No. 5, 209–246 (1986).

    Article  MathSciNet  Google Scholar 

  15. Huppert B. and Lempken W., “Simple groups of order divisible by at most four primes,” Izv. F. Skorina Gomel State Univ., No. 3, 64–75 (2000).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. M. Pal’chik.

Additional information

Original Russian Text Copyright © 2015 Pal’chik E. M.

__________

Novopolotsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 1, pp. 158–164, January–February, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pal’chik, E.M. On the finite groups whose Sylow 3-subgroup normalizes a Sylow 3′-subgroup. Sib Math J 56, 132–137 (2015). https://doi.org/10.1134/S0037446615010139

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446615010139

Keywords

Navigation