This article is cited in 14 papers

Quasivariety lattices of pointed Abelian groups

A. M. Nurakunov

Institute of Theoretical and Applied Mathematics, National Academy of Science of the Kyrgyz Republic, pr. Chui 265a, Bishkek, 720071, Kyrgyzstan

Abstract: We give a description of quasicritical pointed Abelian groups. It is proved that the quasivariety lattice of pointed Abelian groups is $Q$-universal. We construct a quasivariety lattice of pointed Abelian groups whose set of finite sublattices is uncomputable. It is shown that there exists a continuum of such lattices of quasivarieties.

Keywords: quasivariety of algebras, pointed Abelian group, congruence, congruence lattice, quasivariety lattice, Birkhoff–Mal'tsev problem, uncomputable set.

UDC: 512.57

Received: 28.01.2014
Revised: 23.02.2014

 English version: Algebra and Logic, 2014, 53:3, 238–257

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