Skip to main content
Log in

The Occurrence Problem for Subvarieties of the Variety N2A Revisited

  • Published:
Algebra and Logic Aims and scope

Abstract

The occurrence problem in finitely generated subgroups is proved undecidable for groups that are finitely presented in some subvarieties of the variety N 2 A.

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. N. S. Romanovskii, “Occurrence problem for extensions of class 2 nilpotent groups by Abelian groups,” in Proc. 10 All-Union Symp. Group Theory, Gomel (1986), p. 196.

  2. O. G. Kharlampovich, “Algorithmic problems in subvarieties of the variety N 2 A,” in Proc. 8th All-Union Conf. Math. Logic, Moscow (1986), p. 197.

  3. R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin (1977).

    Google Scholar 

  4. N. S. Romanovskii, “Algorithmic problems for solvable groups,” Algebra Logika, 13, No. 1, 26–34 (1974).

    Google Scholar 

  5. N. S. Romanovskii, “Occurrence problem for extensions of Abelian groups by nilpotent groups,” Sib. Mat. Zh., 21, No. 2, 170–174 (1980).

    Google Scholar 

  6. O. G. Kharlampovich, “The word problem in subvarieties of the variety N 2 A,” Algebra Logika, 26, No. 4, 481–501 (1987).

    Google Scholar 

  7. O. G. Kharlampovich, “Finitely presented solvable group with undecidable word problem,” Izv. Akad. Nauk SSSR, Ser. Mat., 45, No. 4, 852–873 (1981).

    Google Scholar 

  8. G. Baumslag, D. Gildenhuys, and R. Strebel, “Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. I,” J. Pure Appl. Alg., 39, Nos. 1/2, 53–94 (1986).

    Google Scholar 

  9. W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory, Interscience, New York (1966).

    Google Scholar 

  10. G. Baumslag, “Subgroups of finitely presented metabelian groups,” J. Austr. Math. Soc., 16, No. 1, 98–110 (1973).

    Google Scholar 

  11. V. N. Remeslennikov, “An example of a finitely presented group in the variety A n, n ⩽ 5, with undecidable word problem,” Algebra Logika, 12, No. 5, 577–602 (1973).

    Google Scholar 

  12. A. I. Mal'tsev, Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Latkin, I.V. The Occurrence Problem for Subvarieties of the Variety N2A Revisited. Algebra and Logic 40, 327–333 (2001). https://doi.org/10.1023/A:1012505919082

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012505919082

Keywords

Navigation