Dominions in Abelian subgroups of metabelian groups

A. I. Budkin

Algebra i logika, Tome 51 (2012) no. 5, pp. 608-622.

Résumé

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.

Détail

Keywords: metabelian group, Abelian subgroup, dominion.

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