Geodesic
A quasivariety lattice of torsion-free soluble groups
Algebra i logika, Tome 50 (2011) no. 3, pp. 368-387.

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

Let $L_q(qG)$ be a lattice of quasivarieties contained in a quasivariety generated by a group $G$. It is proved that if $G$ is a torsion-free finitely generated group in $\mathcal{AB}_{p^k}$, where $p$ is a prime, $p\ne2$, and $k\in\mathbf N$, which is a split extension of an Abelian group by a cyclic group, then the lattice $L_q(qG)$ is a finite chain.
Keywords: quasivariety, quasivariety lattice, metabelian group. 
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A. L. Polushin. A quasivariety lattice of torsion-free soluble groups. Algebra i logika, Tome 50 (2011) no. 3, pp. 368-387. http://geodesic.mathdoc.fr/item/AL_2011_50_3_a4/

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