Skip to main content
SpringerLink
Log in

Structure of finite groups with S-quasinormal third maximal subgroups

  • Published:
Ukrainian Mathematical Journal Aims and scope

We study finite groups whose 3-maximal subgroups are permutable with all Sylow subgroups.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Huppert, “Normalteiler und maximale Untergruppen endlicher Gruppen,” Math. Z., 60, 409–434 (1954).

    Article  MATH  MathSciNet  Google Scholar 

  2. Z. Janko, “Finite groups with invariant fourth maximal subgroups,” Math. Z., 82, 82–89 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  3. Z. Janko, “Finite simple groups with short chains of subgroups,” Math. Z., 84, 428–437 (1964).

    Article  MATH  MathSciNet  Google Scholar 

  4. R. K. Agrawal, “Generalized center and hypercenter of a finite group,” Proc. Amer. Math. Soc., 54, 13–21 (1976).

    Article  Google Scholar 

  5. A. Mann, “Finite groups whose n-maximal subgroups are subnormal,” Trans. Amer. Math. Soc., 132, 395–409 (1968).

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Asaad, “Finite groups some of whose n-maximal subgroups are normal,” Acta Math. Hung., 54, No. 1-2, 9–27 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  7. L. A. Shemetkov, Formations of Finite Groups [in Russian], Nauka, Moscow (1978).

    MATH  Google Scholar 

  8. Yu. V. Lutsenko and A. N. Skiba, “Finite nonnilpotent groups with normal or S-quasinormal n-maximal subgroups,” Izv. Gomel Univ., No. 1(52), 134–138 (2009).

    Google Scholar 

  9. M. Suzuki, “The nonexistence of a certain type of simple groups of odd order,” Proc. Amer. Math. Soc., 8, No. 4, 686–695 (1957).

    Article  MathSciNet  Google Scholar 

  10. Z. Janko, “Endliche Gruppen mit lauter nilpotenten zweitmaximalen Untergruppen,” Math. Z., 79, 422–424 (1962).

    Article  MATH  MathSciNet  Google Scholar 

  11. O. H. Kegel, “Sylow-Gruppen und Subnormalteiler endlicher Gruppen,” Math. Z., 78, 205–221 (1962).

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Gorenstein, Finite Groups, Harper and Row, New York (1968).

    MATH  Google Scholar 

  13. B. Huppert, Endliche Gruppen. I, Springer, Berlin (1967).

    MATH  Google Scholar 

  14. M. Hall, Jr., The Theory of Groups, Macmillan, New York (1959).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Gomel University, Gomel, Belarus

    Yu. V. Lutsenko & A. N. Skiba

Authors
  1. Yu. V. Lutsenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Skiba
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 12, pp. 1630–1639, December, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lutsenko, Y.V., Skiba, A.N. Structure of finite groups with S-quasinormal third maximal subgroups. Ukr Math J 61, 1915–1922 (2009). https://doi.org/10.1007/s11253-010-0322-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-010-0322-x

Keywords

Search

Navigation