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The News of Altai State University
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Management, Computer Facilities and Computer Science
Mathematics and Mechanics
Mathematics and Mechanics

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S.A. Shakhova

On a Property of Intersection Operation in Lattices of Dominions in Quasivarieties of Abelian Groups

The dominion of a subgroup H in a group A (in a class M) is the set of all elements aA such that for all homomorphisms φ, ψ : ABM if φ, ψ coincide on H, then φ(a) = ψ(a). Let A be a group, H be a subgroup of A, Mi(iI) be any quasivarieties of abelian groups and . We find necessary and sufficient conditions when the equality is hold.

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