On coatoms in lattices of quasivarieties of algebraic systems
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It is found the necessary condition for the lattice of quasivarieties has a finite set of coatoms. In particular if a quasivariety is generated by a finitely generated abelian-by-polycyclic-by-finite group or a totally ordered group then it has a finite set of proper maximal subquasivarieties. Also it is proved that the set of quasiverbal congruence relations of a finitely defined universal algebra is closed under any meets.
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