Skip to main content
SpringerLink
Log in

On intersections of solvable Hall subgroups in finite nonsolvable groups

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

The author continues the investigation of intersections of Hall subgroups in finite groups. Previously, the author proved that in the case when a Hall subgroup is Sylow there are three subgroups conjugate to it such that their intersection coincides with the maximal normal primary subgroup. A similar assertion holds for Hall subgroups in solvable groups. The aim of this paper is to construct examples of a (nonsolvable) group in which the intersection of any four subgroups conjugate to some Hall subgroup is nontrivial.

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. D. S. Passman, Trans. Amer. Math. Soc. 123, 99 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. I. Zenkov, Sibirsk. Mat. Zh. 34(4), 103 (1993).

    MathSciNet  Google Scholar 

  3. E. P. Vdovin, Sib. Electronic Math. Reports 4, 345 (2007).

    MATH  Google Scholar 

  4. V. I. Zenkov, Fund. Prikl. Mat. 2(1), 1 (1996).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Ekaterinburg, 620219, Russia

    V. I. Zenkov

Authors
  1. V. I. Zenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.I. Zenkov, 2007, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2007, Vol. 13, No. 2.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zenkov, V.I. On intersections of solvable Hall subgroups in finite nonsolvable groups. Proc. Steklov Inst. Math. 259 (Suppl 2), S250–S253 (2007). https://doi.org/10.1134/S0081543807060181

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543807060181

Keywords

Search

Navigation