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Algebra and Logic

, Volume 58, Issue 3, pp 232–243 | Cite as

Canonical and Algebraically Closed Groups in Universal Classes of Abelian Groups

  • A. A. MishchenkoEmail author
  • V. N. Remeslennikov
  • A. V. Treier
Article

Using sets of finitely generated Abelian groups closed under the discrimination operator, we describe principal universal classes 𝒦 within a quasivariety 𝔄p, the class of groups whose periodic part is a p-group for a prime p. Also the concept of an algebraically closed group in 𝒦 is introduced, and such groups are classified.

Keywords

Abelian group universal class principal universal class canonical group discriminability of classes of groups 𝒦-algebraically closed groups ladder vector 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. A. Mishchenko
    • 1
    Email author
  • V. N. Remeslennikov
    • 2
  • A. V. Treier
    • 2
  1. 1.Sobolev Institute of MathematicsOmskRussia
  2. 2.Sobolev Institute of MathematicsOmskRussia

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