Algebra and Logic

, Volume 35, Issue 3, pp 172–175 | Cite as

The arithmetical hierarchy of nilpotent torsion-free groups

  • I. V. Latkin


Previously, N. Khisamiev proved that all {ie172-1} Abelian torsion-free groups are {ie172-2}. We prove that for the class of nilpotent torsion-free groups, the situation is different: even the quotient group F of a {ie172-3} nilpotent group of class 2 by its periodic part may fail to have a {ie172-4}.


Mathematical Logic Nilpotent Group Quotient Group Periodic Part Arithmetical Hierarchy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yu. L. Ershov,Decidability Problems and Constructive Models [in Russian], Nauka, Moscow (1980).Google Scholar
  2. 2.
    H. Rogers,Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).Google Scholar
  3. 3.
    A. I. Mal'tsev, “Recursive Abelian groups,”Dokl. Akad. Nauk SSSR,24, No. 2, 1009–1012 (1962).Google Scholar
  4. 4.
    A. T. Nurtasin, “On constructive groups,” inProc. IV All-Union Conf. Math. Logic, Kishinev (1976), p. 106.Google Scholar
  5. 5.
    V. P. Dobritsa, “Some constructivizations of Abelian groups,”Sib. Mat. Zh.,24, No. 2, 18–25 (1983).MATHMathSciNetGoogle Scholar
  6. 6.
    N. G. Khisamiev, “Hierarchies of torsion-free Abelian groups,”Algebra Logika,25, No. 2, 205–226 (1986).MATHMathSciNetGoogle Scholar
  7. 7.
    W. Magnus, A. Karrass, and D. Solitar,Combinatorial Group Theory, Interscience, New York (1966).Google Scholar
  8. 8.
    O. N. Golovin, “Nilpotent products of groups,”Mat. Sb.,27, 427–454 (1950).MATHMathSciNetGoogle Scholar
  9. 9.
    T. MacHenry, “The tensor product and the 2-nd nilpotent product of groups,”Math. J.,73, 134–145 (1960).MATHMathSciNetGoogle Scholar
  10. 10.
    I. V. Latkin, “The hierarchy of torsion-free nilpotent groups,” inProc. IX All-Union Conf. Math. Logic, Leningrad (1988), p. 91.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • I. V. Latkin

There are no affiliations available

Personalised recommendations