Dominions in quasivarieties of metabelian groups |
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Authors: | A I Budkin |
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Institution: | 1.Alta? State University,Barnaul,Russia |
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Abstract: | The dominion of a subgroup H of a group A in a quasivariety ℳ is the set of all a ∈ A with equal images under all pairs of homomorphisms from A into every group in ℳ which coincide on H. The concept of dominion provides some closure operator on the lattice of subgroups of a given group. We study the closed
subgroups with respect to this operator. We find a condition for the dominion of a divisible subgroup in quasivarieties of
metabelian groups to coincide with the subgroup. |
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