Algebra and Logic

, Volume 46, Issue 4, pp 219–230 | Cite as

The quasivariety generated by a torsion-free Abelian-by-finite group

  • A. I. Budkin


Let Lq(qG) be the quasivariety lattice contained in a quasivariety generated by a group G. It is proved that if G is a finitely generated torsion-free group in \(\mathcal{A}\mathcal{B}_{2^n } \) (i.e., G is an extension of an Abelian group by a group of exponent 2n), which is a split extension of an Abelian group by a cyclic group, then the lattice Lq(qG) is a finite chain.


quasivariety quasivariety lattice metabelian group 


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© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • A. I. Budkin
    • 1
  1. 1.BarnaulRussia

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