On a cardinality of the lattice of quasivarieties of nilpotent groups
Copyright policy )On a cardinality of the lattice of quasivarieties of nilpotent groups
Given a class \(\mathcal R\) of groups, denote by \(q{\mathcal R}\) the quasivariety generated by this class. Let \(L_{q}(q{\mathcal R})\) be the lattice of quasivarieties contained in \(q{\mathcal R}\). The author computes the cardinality of the lattice of quasivarieties \(L_{q}(q{\mathcal N})\) for every quasivariety \(\mathcal N\) of nilpotent groups of class 2. This result generalizes theorems by the author published in Sib. Adv. Math. 7, No. 3, 98-125 (1997; Zbl 0917.20026).
nilpotent group, Lattices of varieties, Nilpotent groups, lattice of quasivarieties, Quasivarieties, Quasivarieties and varieties of groups
nilpotent group, Lattices of varieties, Nilpotent groups, lattice of quasivarieties, Quasivarieties, Quasivarieties and varieties of groups
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