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


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Last modified: November 11, 1999