Geodesic
Quasivariety lattices of pointed Abelian groups
Algebra i logika, Tome 53 (2014) no. 3, pp. 372-400

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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. 
@article{AL_2014_53_3_a4,
     author = {A. M. Nurakunov},
     title = {Quasivariety lattices of pointed {Abelian} groups},
     journal = {Algebra i logika},
     pages = {372--400},
     publisher = {mathdoc},
     volume = {53},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2014_53_3_a4/}
}
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A. M. Nurakunov. Quasivariety lattices of pointed Abelian groups. Algebra i logika, Tome 53 (2014) no. 3, pp. 372-400. http://geodesic.mathdoc.fr/item/AL_2014_53_3_a4/