Algebra and Logic

, 50:1 | Cite as

Universal theories for partially commutative metabelian groups


We look at properties of partially commutative metabelian groups and of their universal theories. In particular, it is shown that two partially commutative metabelian groups defined by cycles are universally equivalent if and only if the cycles are isomorphic.


partially commutative metabelian group universal theory 


  1. 1.
    Ch. K. Gupta and E. I. Timoshenko, “Partially commutative metabelian groups: Centralizers and elementary equivalence,” Algebra Logika, 48, No. 3, 309–341 (2009).MathSciNetGoogle Scholar
  2. 2.
    E. I. Timoshenko, “Universal equivalence of partially commutative metabelian groups,” Algebra Logika, 49, No. 2, 363–289 (2010).MathSciNetGoogle Scholar
  3. 3.
    A. J. Duncan, I. V. Kazachkov, and V. N. Remeslennikov, “Orthogonal systems in finite graphs,” Sib. El. Mat. Izv., 5, 151–176 (2008).MathSciNetGoogle Scholar
  4. 4.
    V. N. Remeslennikov, and A. V. Treier, “Structure of the automorphism group for partially commutative class two nilpotent groups,” Algebra Logika, 49, No. 1, 60–97 (2010).MathSciNetGoogle Scholar
  5. 5.
    V. N. Remeslennikov and N. S. Romanovskii, “Metabelian products of groups,” Algebra Logika, 43, No. 3, 341–352 (2004).MATHMathSciNetGoogle Scholar
  6. 6.
    A. H. Rhemtulla, “Commutators of certain finitely generated soluble groups,” Can. J. Math., 21, No. 5, 1160–1164 (1969).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.University of ManitobaWinnipegCanada
  2. 2.Novosibirsk State Technical UniversityNovosibirskRussia

Personalised recommendations