Skip to main content
SpringerLink
Log in

Finite Sylow Subgroups in Simple Locally Finite Groups of Lie Type

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

The main result of the paper is the following

Theorem. Let S = {r0, r1, ..., rn} be a finite nonempty set of primes and let L be a Lie type of Chevalley groups. Then there exists a locally finite field F of characteristic r0 such that Sylow r-subgroups of the simple group L(F) of type L over F are finite if and only if r ∉ S.

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. Hartley B. and Shute G., “Monomorphisms and direct limits of finite groups of Lie type,” Quart. J. Math. (2), 33, 309–323 (1982).

    Google Scholar 

  2. Brawley J. V. and Schnibben G. E., Infinite Algebraic Extensions of Finite Fields, Amer. Math. Soc., Providence, RI (1989). (Contemporary Mathematics; V. 95.)

  3. Dixon M. R., Sylow Theory, Formations and Fitting Classes in Locally Finite Groups, World Sci., Singapore (1994). (Ser. Algebra; V. 2.)

  4. 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).

    Google Scholar 

  5. Zsigmondy K., “Zur Theorie der Potenzreste,” Monatsh. Math. Phys., Bd 3, 265–284 (1892).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Middle East Technical University, Ankara, Turkey

    M. Kuzucuoglu

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. D. Mazurov

Authors
  1. M. Kuzucuoglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. D. Mazurov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text Copyright © 2005 Kuzucuoglu M. and Mazurov V. D.

The authors were supported by the Russian Foundation for Basic Research (Grant 05-01-00797), a grant of the Presidium of the Siberian Branch of the Russian Academy of Sciences (No.86-197), the Program “Universities of Russia” (Grant UR.04.01.028), the Program “Development of the Scientific Potential of Higher School” of the Ministry for Education of the Russian Federation (Grant 511), and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2069.2003.1).

__________

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 1079–1084, September–October, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuzucuoglu, M., Mazurov, V.D. Finite Sylow Subgroups in Simple Locally Finite Groups of Lie Type. Sib Math J 46, 863–866 (2005). https://doi.org/10.1007/s11202-005-0084-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-005-0084-0

Keywords

Search

Navigation