Skip to main content
SpringerLink
Log in

Groups with the quasicyclic centralizer of a finite involution

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We prove that a group with the not maximal quasicyclic centralizer of a finite involution is locally finite.

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. Adian S. I., The Burnside Problem and Identities in Groups, Springer-Verlag, Berlin and New York (1978).

    Google Scholar 

  2. Sozutov A. I. and Durakov E. B., “Two questions in The Kourovka Notebook,” Algebra and Logic, 52, No. 5, 422–425 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  3. Mazurov V. D., Ol’shanskiĭ A. Yu., and Sozutov A. I., “Infinite groups of finite period,” Algebra and Logic, 54, No. 2, 161–166 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  4. Mazurov V. D., “Infinite groups with Abelian centralizers of involutions,” Algebra and Logic, 39, No. 1, 42–49 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  5. Sozutov A. I., “Some infinite groups with strongly embedded subgroup,” Algebra and Logic, 39, No. 5, 345–353 (2000).

    Article  MathSciNet  Google Scholar 

  6. Sozutov A. I. and Suchkov N. M., “On infinite groups with a given strongly isolated 2-subgroup,” Math. Notes, 68, No. 2, 237–247 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  7. Suchkov N. M., “On periodic groups with Abelian centralizers of involution,” Sb. Math., 193, No. 2, 303–310 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  8. Mazurov V. D. and Khukhro E. I. (Eds.), The Kourovka Notebook: Unsolved Problems in Group Theory, 15th ed., Sobolev Inst. Math., Novosibirsk (2002).

    MATH  Google Scholar 

  9. Sozutov A. I., Suchkov N. M., and Suchkova N. G., Infinite Groups with Involutions, Sib. Fed. Univ., Krasnoyarsk (2011).

    Google Scholar 

  10. Belyaev V. V., “Groups with an almost-regular involution,” Algebra and Logic, 26, No. 5, 315–317 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  11. Sozutov A. I., “Groups with an almost regular involution,” Algebra and Logic, 46, No. 3, 195–199 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  12. Kargapolov M. I. and Merzlyakov Yu. I., Fundamentals of the Theory of Groups, Springer-Verlag, New York, Heidelberg, and Berlin (1979).

    Book  MATH  Google Scholar 

  13. Ito N., “Über das Product von zwei abelschen Gruppen,” Math. Z., Bd 62, Heft 4, 400–401 (1955).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Siberian State Aerospace University, Krasnoyarsk, Russia

    A. I. Sozutov

Authors
  1. A. I. Sozutov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Sozutov.

Additional information

The author was supported by the Russian Foundation for Basic Research (Grant 15–01–04897-a).

Krasnoyarsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 5, pp. 11127–1130, September–October, 2016; DOI: 10.17377/smzh.2016.57.518.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sozutov, A.I. Groups with the quasicyclic centralizer of a finite involution. Sib Math J 57, 881–883 (2016). https://doi.org/10.1134/S0037446616050189

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446616050189

Keywords

Search

Navigation