Skip to main content
Log in

Zenkov Hypothesis on Pair p-Sylow Intersections of Chevalley Groups of Characteristic p

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We present all Chevalley groups over a finite field of arbitrary characteristic p in which the index of the normalizer of any pair of Sylow p-subgroups is relatively prime with p.

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. Kourovka Notebook (Unsolved Problems in Group Theory) [in Russian], Institute of Mathematics, Russian Academy of Sciences, Siberian Division, Novosibirsk (1999).

  2. V. I. Zenkov, Intersections of Nilpotent Subgroups in Finite Groups [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Krasnoyarsk (1996).

  3. T. Yu. Voitenko and V. M. Levchuk, “Zenkov hypothesis on pair p-Sylow intersections of Chevalley groups of characteristic p,” in: Abstracts of the International Seminar on Group Theory Dedicated to the 70th Birthday of A. I. Starostin and the 80th Birthday of N. G. Sesekin [in Russian], Ural University, Ekaterinburg (2001), pp. 55–57.

    Google Scholar 

  4. T. Yu. Voitenko, “Zenkov hypothesis on pair p-Sylow intersections of Chevalley groups of characteristic p,” in: Abstracts of the Second All-Siberian Congress of Women-Mathematicians [in Russian], Krasnoyarsk University, Krasnoyarsk (2002), pp. 40–41.

    Google Scholar 

  5. T. Yu. Voitenko and V. M. Levchuk, “Pair unipotent intersections of Chevalley groups of small Lie ranks,” in: Symmetry and Differential Equations [in Russian], Institute of Computational Mathematics, Russian Academy of Sciences, Siberian Division, Krasnoyarsk (2000), pp. 71–74.

    Google Scholar 

  6. T. Yu. Voitenko, “Pair Sylow intersections of Chevalley groups of Lie rank 3,” in: Investigations in Mathematical Analysis and Algebra [in Russian], Issue 3, Tomsk University, Tomsk (2001), pp. 21–27.

    Google Scholar 

  7. T. Yu. Voitenko, “Pair unipotent intersections of Chevalley groups of the types E l,” in: Collection of Works [in Russian], Krasnoyarsk University, Krasnoyarsk (2001), pp. 32–40.

    Google Scholar 

  8. R. Carter, Simple Groups of Lie Type, Wiley, New York (1972).

    Google Scholar 

  9. V. V. Kabanov and A. S. Kondrat'ev, Sylow 2-Subgroups of Finite Groups [in Russian], Institute of Mathematics and Mechanics, Academy of Sciences of the USSR, Ural Scientific Center, Sverdlovsk (1979).

    Google Scholar 

  10. V. M. Levchuk, “Hypercentral series and pair intersections of Sylow subgroups of Chevalley groups,” Algebra Logika, 41, No. 4, 567–578 (2002).

    Google Scholar 

  11. N. Bourbaki, Groupes et Algèbres de Lie, Chaps. IV–VI, Hermann, Paris (1968).

    Google Scholar 

  12. V. M. Levchuk, “Automorphisms of unipotent subgroups of groups of the Lie type of small ranks,” Algebra Logika, 29, No. 2, 141–161 (1990).

    Google Scholar 

  13. V. M. Levchuk, “Automorphisms of unipotent subgroups of Chevalley groups,” Algebra Logika, 29, No. 3, 315–338 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voitenko, T.Y., Levchuk, V.M. Zenkov Hypothesis on Pair p-Sylow Intersections of Chevalley Groups of Characteristic p. Ukrainian Mathematical Journal 54, 1098–1111 (2002). https://doi.org/10.1023/A:1022010308251

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022010308251

Keywords

Navigation