Skip to main content
SpringerLink
Log in

Cocyclic n-groups

  • Brief communication
  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We describe all cocyclic n-groups and the structure of (n, 2)-rings of endomorphisms of cocyclic n-groups. We prove that a cocyclic n-group is defined uniquely by its (n, 2)-ring of endomorphisms.

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. Gal’mak, A.M. n-ary Groups (F. Skaryna Gomel State Univ., Gomel, 2003), Part 1 [in Russian].

    MATH  Google Scholar 

  2. Post, E. L. “Polyadic Groups”, Trans.Amer.Math. Soc. 48, 208–350 (1940).

    Article  MathSciNet  MATH  Google Scholar 

  3. Rusakov, S. A. Algebraic n-ary Systems (Navuka i tekhnika, Minsk, 1992) [in Russian].

    Google Scholar 

  4. Rusakov, S. A. Some Applications of the Theory of n-ary Groups (Belarussk. navuka, Minsk, 1998) [in Russian].

    Google Scholar 

  5. Timm J. “Kommutative n-Gruppen” (Diss., Hamburg, 1967).

    Google Scholar 

  6. Gal’mak, A. M. “Polyadic Analogs of the Cayley and Birkhoff Theorems”, Russian Mathematics 45, No. 2, 10–15 (2001).

    MathSciNet  MATH  Google Scholar 

  7. Glazek, K., Michalski, J., Sierocki, A. I. “On Evaluation of Some Polyadic Groups”, Contributions to General Algebra 3, 159–171 (1985).

    MATH  Google Scholar 

  8. Shchuchkin, N. A. “Semi-cyclic n-ary Groups”, Izv. F. SkarynaUniv. 3, 186–194 (2009) [in Russian].

    Google Scholar 

  9. Shchuchkin, N. A. “Subgroups of Semi-Cyclic n-ary Groups”, Journal of Mathematical Sciences 167, No. 6, 870–877 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  10. Gal’mak, A. M., Shchuchkin, N. A. “Cyclic n-ary Groups and Their Generalizations”, Probl. Fiziki, Mat. and Tekhn. 2, 46–53 (2014) [in Russian].

    MATH  Google Scholar 

  11. Shchuchkin, N. A. “The Structure of Finite Abelian n-ary Groups”, Discrete Math. Appl. 25, No. 1, 47–58 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  12. Shchuchkin, N. A. “Free Abelian n-ary Groups”, Chebyshevskii Sb. 2, 163–170 (2011) [in Russian].

    MathSciNet  MATH  Google Scholar 

  13. Fuchs, L. Infinite Abelian Groups (Academic Press, New York–London, 1970;Mir,Moscow, 1974), Vol. 1.

    MATH  Google Scholar 

  14. Kurosh, A. G. General Algebra. Lectures for the Academic Year 1969–1970 (Nauka, Moscow, 1974) [in Russian].

    MATH  Google Scholar 

  15. Glazek, K. and Gleichgewicht, B. “Abelian n-Groups”, Colloquia Math. Soc. J. Bolyai 29, 321–329 (1977).

    MATH  Google Scholar 

  16. Crombez, G. “On (n,m)-Rings”, Abh. Math. Sem.Univ. Hamburg 37, 180–199 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  17. Fuchs, L. Infinite Abelian Groups (Academic Press, New York–London, 1973;Mir,Moscow, 1977), Vol. II.

    Google Scholar 

  18. Khodabandeh, H., Shahryari, M. “Simple Polyadic Groups”, SiberianMathematical Journal 55, No. 4, 734–744 (2014).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Volgograd State Socio-Pedagogical University, pr. Lenina 27, Volgograg, 400131, Russia

    N. A. Shchuchkin

Authors
  1. N. A. Shchuchkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. A. Shchuchkin.

Additional information

Original Russian Text © N.A. Shchuchkin, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 10, pp. 89–93.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shchuchkin, N.A. Cocyclic n-groups. Russ Math. 61, 77–81 (2017). https://doi.org/10.3103/S1066369X17100115

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X17100115

Keywords

Search

Navigation