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Dominions in abelian subgroups of metabelian groups

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Algebra and Logic Aims and scope

It is proved that a suitable free Abelian group of finite rank is not absolutely closed in the class \( {\mathcal A} \) 2 of metabelian groups. A condition is specified under which a torsion-free Abelian group is not absolutely closed in \( {\mathcal A} \) 2. Also we gain insight into the question when the dominion in \( {\mathcal A} \) 2 of the additive group of rational numbers coincides with this subgroup.

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  1. Pavlovskii road, 60a-168, Barnaul, 656064, 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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Translated from Algebra i Logika, Vol. 51, No. 5, pp. 608-622, September-October, 2012.

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Budkin, A.I. Dominions in abelian subgroups of metabelian groups. Algebra Logic 51, 404–414 (2012). https://doi.org/10.1007/s10469-012-9200-y

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  • DOI: https://doi.org/10.1007/s10469-012-9200-y

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