Algebra and Logic

, Volume 51, Issue 3, pp 259–263 | Cite as

Universal theories for free solvable groups

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It is proved that a free solvable group of derived length at least 4 has an algorithmically undecidable universal theory.

Keywords

universal theory decidable theory free solvable group 
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References

  1. 1.
    A. I. Mal’tsev, “Free solvable groups,” Dokl. Akad. Nauk SSSR, 130, No. 3, 495-498 (1960).Google Scholar
  2. 2.
    O. Chapuis, “Universal theory of certain solvable groups and bounded Ore group rings,” J. Alg., 176, No. 2, 368-391 (1995).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    O. Chapuis, “∀-free metabelian groups,” J. Symb. Log., 62, No. 1, 159-174 (1997).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    V. Remeslennikov and R. Stohr, “On the quasivariety generated by a non-cyclic free metabelian group,” Alg. Colloq., 11, No. 2, 191-214 (2004).MathSciNetMATHGoogle Scholar
  5. 5.
    O. Chapuis, “On the theories of free solvable groups,” J. Pure Appl. Alg., 131, No. 1, 13-24 (1998).MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Yu. V. Matiyasevich, “Being Diophantine for enumerable sets,” Dokl. Akad. Nauk SSSR, 191, No. 2, 279-282 (1970).MathSciNetGoogle Scholar
  7. 7.
    N. S. Romanovskii, “Shmel’kin embeddings for abstract and profinite groups,” Algebra Logika, 38, No. 5, 598-612 (1999).MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. G. Myasnikov and N. S. Romanovskii, “Universal theories for rigid soluble groups,” Algebra Logika, 50, No. 6, 802-821 (2011).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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