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Universal theories for free solvable groups

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Algebra and Logic Aims and scope

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

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References

  1. A. I. Mal’tsev, “Free solvable groups,” Dokl. Akad. Nauk SSSR, 130, No. 3, 495-498 (1960).

    Google Scholar 

  2. O. Chapuis, “Universal theory of certain solvable groups and bounded Ore group rings,” J. Alg., 176, No. 2, 368-391 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  3. O. Chapuis, “∀-free metabelian groups,” J. Symb. Log., 62, No. 1, 159-174 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  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).

    MathSciNet  MATH  Google Scholar 

  5. O. Chapuis, “On the theories of free solvable groups,” J. Pure Appl. Alg., 131, No. 1, 13-24 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  6. Yu. V. Matiyasevich, “Being Diophantine for enumerable sets,” Dokl. Akad. Nauk SSSR, 191, No. 2, 279-282 (1970).

    MathSciNet  Google Scholar 

  7. N. S. Romanovskii, “Shmel’kin embeddings for abstract and profinite groups,” Algebra Logika, 38, No. 5, 598-612 (1999).

    Article  MathSciNet  Google Scholar 

  8. A. G. Myasnikov and N. S. Romanovskii, “Universal theories for rigid soluble groups,” Algebra Logika, 50, No. 6, 802-821 (2011).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    N. S. Romanovskii

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    N. S. Romanovskii

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  1. N. S. Romanovskii
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Correspondence to N. S. Romanovskii.

Additional information

Supported by RFBR, grant No. 12-01-00084.

Translated from Algebra i Logika, Vol. 51, No. 3, pp. 385-391, May-June, 2012.

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Romanovskii, N.S. Universal theories for free solvable groups. Algebra Logic 51, 259–263 (2012). https://doi.org/10.1007/s10469-012-9188-3

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  • DOI: https://doi.org/10.1007/s10469-012-9188-3

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