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The Lattice of Subvarieties of the Variety Defined by Externally Compatible Identities of Abelian Groups of Exponent n

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Abstract

The lattices of varieties were studied in many works (see [4], [5], [11], [24], [31]). In this paper we describe the lattice of all subvarieties of the variety \(\mathcal{G}^{n}_{Ex}\) defined by so called externally compatible identities of Abelian groups and the identity xn ≈ yn.

The notation in this paper is the same as in [2].

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Correspondence to Krystyna Mruczek-Nasieniewska.

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Gajewska-Kurdziel, K., Mruczek-Nasieniewska, K. The Lattice of Subvarieties of the Variety Defined by Externally Compatible Identities of Abelian Groups of Exponent n . Stud Logica 85, 361–379 (2007). https://doi.org/10.1007/s11225-007-9038-9

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Keywords

  • Abelian groups
  • identity
  • externally compatible identity
  • variety

Mathematics Subject Classification

  • 03C05
  • 20A05