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Fundamentals of the theory of varieties of nilpotent MR-groups

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Abstract

We expose fundamentals of the theory of varieties of nilpotent MR-groups and compare various definitions of nilpotency in this category.

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References

  1. Lyndon R. C., “Groups with parametric exponents,” Trans. Amer. Math. Soc., 96, 518–533 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  2. Myasnikov A. G. and Remeslennikov V. N., “Groups with exponents. I: Fundamentals of the theory and tensor completions,” Sib. Math. J., 35, No. 5, 986–996 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  3. Myasnikov A. G. and Remeslennikov V. N., “Exponential groups. II. Extensions of centralizers and tensor completion of CSA-groups,” Int. J. Algebra Comput., 6, No. 6, 687–711 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  4. Baumslag G., Myasnikov A., and Remeslennikov V., “Discriminating completions of hyperbolic groups,” Dedicated to John Stallings on the occasion of his 65th birthday. Geom. Dedicata, 92, 115–143 (2002).

    MathSciNet  MATH  Google Scholar 

  5. Amaglobeli M. G. and Bokelavadze T. Z., “Groups with exponents. Groups which are exact under tensor completion,” Vestn. Omsk Univ., 2, 35–46 (2009).

    MATH  Google Scholar 

  6. Amaglobeli M. G. and Remeslennikov V. N., “Free nilpotent R-groups of class 2,” Dokl. Akad. Nauk, 443, No. 4, 410–413 (2012).

    MathSciNet  MATH  Google Scholar 

  7. Amaglobeli M. G. and Remeslennikov V. N., “Centralizer extension in nilpotent groups,” Sib. Math. J., 54, No. 1, 1–9 (2013).

    MathSciNet  MATH  Google Scholar 

  8. Amaglobeli M. and Remeslennikov V., “Algorithmic problems for class-2 nilpotent MR-groups,” Georgian Math. J., 22, No. 4, 441–449 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  9. Baumslag G., “Free abelian X-groups,” Illinois J. Math., 30, No. 2, 235–245 (1986).

    MathSciNet  MATH  Google Scholar 

  10. Hall P., “Nilpotent groups,” Matematika, 12, No. 1, 3–36 (1968).

    MathSciNet  Google Scholar 

  11. Kargapolov M. I. and Merzlyakov Yu. I., Fundamentals of the Theory of Groups, Springer-Verlag, New York, Heidelberg, and Berlin (1979).

    Book  MATH  Google Scholar 

  12. Gorbunov V. A., Algebraic Theory of Quasivarieties, Plenum, New York (1998).

    MATH  Google Scholar 

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Correspondence to M. G. Amaglobeli.

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Original Russian Text Copyright © 2016 Amaglobeli M.G. and Remeslennikov V.N.

The results of §3 and § 4 were supported by the Russian Foundation for Basic Research (Grant 14–01–00068). The other results were supported by the Russian Science Foundation (Grant 14–11–00085).

To the 70th anniversary of N. S. Romanovskiĭ.

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Amaglobeli, M.G., Remeslennikov, V.N. Fundamentals of the theory of varieties of nilpotent MR-groups. Sib Math J 57, 935–942 (2016). https://doi.org/10.1134/S003744661606001X

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  • DOI: https://doi.org/10.1134/S003744661606001X

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