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. 
@article{AL_2005_44_4_a0,
     author = {A. I. Budkin},
     title = {Quasivariety {Generated} by {Free} {Metabelian} and {2-Nilpotent} {Groups}},
     journal = {Algebra i logika},
     pages = {389--398},
     publisher = {mathdoc},
     volume = {44},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2005_44_4_a0/}
}
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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/