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Dominions in quasivarieties of metabelian groups

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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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Authors and Affiliations

  1. Altaĭ State University, Barnaul, Russia

    A. I. Budkin

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  1. A. I. Budkin
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Correspondence to A. I. Budkin.

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Original Russian Text Copyright © 2010 Budkin A. I.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 498–505, May–June, 2010.

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Budkin, A.I. Dominions in quasivarieties of metabelian groups. Sib Math J 51, 396–401 (2010). https://doi.org/10.1007/s11202-010-0040-5

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  • DOI: https://doi.org/10.1007/s11202-010-0040-5

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