Geodesic
Dominions in Abelian subgroups of metabelian groups
Algebra i logika, Tome 51 (2012) no. 5, pp. 608-622

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{AL_2012_51_5_a2,
     author = {A. I. Budkin},
     title = {Dominions in {Abelian} subgroups of metabelian groups},
     journal = {Algebra i logika},
     pages = {608--622},
     publisher = {mathdoc},
     volume = {51},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2012_51_5_a2/}
}
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A. I. Budkin. Dominions in Abelian subgroups of metabelian groups. Algebra i logika, Tome 51 (2012) no. 5, pp. 608-622. http://geodesic.mathdoc.fr/item/AL_2012_51_5_a2/