Geodesic
On full residuance of some groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 871-883 
P. V. Ushakov. On full residuance of some groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 871-883. http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a16/
@article{FPM_1999_5_3_a16,
     author = {P. V. Ushakov},
     title = {On full residuance of some groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {871--883},
     year = {1999},
     volume = {5},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a16/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we define the rank of a finitely generated torsion free nilpotent group. The main result is the following Theorem. Let $G$ be a finitely generated nilpotent group. Let $\mathfrak U$ be an arbitrary variety of groups. Assume that $G$ is torsion free, $\operatorname{rk}G=k$, $\mathfrak N:=\operatorname{var}G$, $G\cong F_k/R$, $R\triangleleft F_k$. Then for all $s>k$, the groups $F_s(\mathfrak{UN})$ are fully residual $F_k/U(R)$-groups.