Siberian Mathematical Journal

, Volume 48, Issue 1, pp 3–7 | Cite as

Algebraic sets and coordinate groups for a free nilpotent group of nilpotency class 2

  • M. G. Amaglobeli
Article

Abstract

We give a complete classification of the algebraic sets and coordinate groups for the systems of equations in one variable over a free nilpotent group.

Keywords

algebraic geometry over a group algebraic set coordinate group 

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References

  1. 1.
    Appel K. I., “One-variable equations in free groups,” Proc. Amer. Math. Soc., 19, 912–918 (1968).CrossRefMathSciNetGoogle Scholar
  2. 2.
    Lorents A. A., “The solution of systems of equations in one unknown in free groups,” Soviet Math. Dokl., 4, 262–265 (1963).Google Scholar
  3. 3.
    Lorents A. A., “Equations without coefficients in free groups,” Soviet Math. Dokl., 6, 141–143 (1965).Google Scholar
  4. 4.
    Lyndon R. C., “Equations in free groups,” Trans. Amer. Math. Soc., 96, 445–457 (1960).CrossRefMathSciNetGoogle Scholar
  5. 5.
    Chiswell I. M. and Remeslennikov V. N., “Equations in free groups with one variable. I,” J. Group Theory, 3, No. 4, 445–466 (2000).CrossRefMathSciNetGoogle Scholar
  6. 6.
    Chapuis O., “∀-free metabelian groups,” J. Symbolic Logic, 62, No. 1, 159–174 (1997).CrossRefMathSciNetGoogle Scholar
  7. 7.
    Remeslennikov V. and Stöhr R., “On the quasivariety generated by a non-cyclic free metabelian group,” Algebra Colloq., 11, No. 2, 191–214 (2004).MathSciNetGoogle Scholar
  8. 8.
    Remeslennikov V. N. and Romanovskii N. S., “Metabelian products of groups,” Algebra and Logic, 43, No. 3, 190–197 (2004).CrossRefMathSciNetGoogle Scholar
  9. 9.
    Remeslennikov V. N. and Romanovskii N. S., “Irreducible algebraic sets in a metabelian group,” Algebra and Logic, 44, No. 5, 336–347 (2005).CrossRefMathSciNetGoogle Scholar
  10. 10.
    Amaglobeli M. G., “G-identities of nilpotent groups. I,” Algebra and Logic, 40, No. 1, 1–11 (2001).CrossRefMathSciNetGoogle Scholar
  11. 11.
    Baumslag G., Myasnikov A., and Remeslennikov V., “Algebraic geometry over groups. I. Algebraic sets and ideal theory,” J. Algebra, 219, No. 1, 16–79 (1999).CrossRefMathSciNetGoogle Scholar
  12. 12.
    Myasnikov A. and Remeslennikov V., “Algebraic geometry over groups. II. Logical foundations,” J. Algebra, 234, No. 1, 225–276 (2000).CrossRefMathSciNetGoogle Scholar
  13. 13.
    Neumann H., Varieties of Groups, Springer-Verlag, Berlin; Heidelberg; New York (1967).MATHGoogle Scholar
  14. 14.
    Amaglobeli M. G. and Remeslennikov V. N., “G-identities and G-varieties,” Algebra and Logic, 39, No. 3, 141–154 (2000).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • M. G. Amaglobeli
    • 1
  1. 1.Tbilisi State UniversityTbilisiGeorgia

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