Scientific journal "The News of Altai State University". 2010 #1-1(65). Mathematics and Mechanics.

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1-1(65)

2010

$Mathematics and Mechanics$

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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 a ∈ A such that for all homomorphisms φ, ψ : A → B ∈ M if φ, ψ coincide on H, then φ(a) = ψ(a). Let A be a group, H be a subgroup of A, M_i(i ∈ I) be any quasivarieties of abelian groups and

. We find necessary and sufficient conditions when the equality

is hold.

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