Geodesic
Quasivariety Generated by Free Metabelian and 2-Nilpotent Groups
Algebra i logika, Tome 44 (2005) no. 4, pp. 389-398.

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

Let $qG$ be a quasivariety generated by a group $G$ and $\mathcal N$ be a non-Abelian quasivariety of groups with a finite lattice of subquasivarieties. Suppose $\mathcal N$ is contained in a quasivariety generated by the following two groups: a free $2$-nilpotent group $F_2(\mathcal N_2)$ of rank 2 and a free metabelian (i. e., with an Abelian commutant) group $F_2(\mathcal A^2)$ of rank 2. It is proved that either $\mathcal N=q F_2(\mathcal N_2)$ or $\mathcal N=q F_2(\mathcal A^2)$ in this instance.
Keywords: quasivariety, free group, metabelian group, 2-nilpotent group. 
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A. I. Budkin. Quasivariety Generated by Free Metabelian and 2-Nilpotent Groups. Algebra i logika, Tome 44 (2005) no. 4, pp. 389-398. http://geodesic.mathdoc.fr/item/AL_2005_44_4_a0/

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