FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 3, PAGES 871-883

## On full residuance of some groups

P. V. Ushakov

Abstract

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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, $\mathop\left\{\mathrm\left\{rk\right\}\right\} G=k$, $\mathfrak N := \mathop\left\{\mathrm\left\{var\right\}\right\} G$, $G$@ Fk/R, $R \triangleleft F_k$. Then for all $s > k$, the groups $F_s\left(\mathfrak \left\{UN\right\}\right)$ are fully residual $F$k/U(R)-groups.

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