FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1999, VOLUME 5, NUMBER 3, PAGES 871-883
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
\textbf{Theorem.} Let
$G$ be a finitely
generated nilpotent
group. Let $\mathfrak U$
be an arbitrary variety of groups.
Assume that $G$ is torsion free,
$\mathop{\mathrm{rk}} G=k$ ,
$\mathfrak N :=
\mathop{\mathrm{var}} G$ ,
$G\cong F_k/R$ ,
$R\triangleleft F_k$ .
Then for all $s>k$ ,
the groups
$F_s(\mathfrak{UN})$
are fully residual
$F_k/U(R)$ -groups.
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Last modified: November 11, 1999