This article is cited in 5 papers

Dominions in Abelian subgroups of metabelian groups

A. I. Budkin

Barnaul, Russia

Abstract: 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.

Keywords: metabelian group, Abelian subgroup, dominion.

UDC: 512.57

Received: 18.06.2012
Revised: 28.09.2012

 English version: Algebra and Logic, 2012, 51:5, 404–414

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