This article is cited in 21 papers

The property of being equationally Noetherian for some soluble groups

Ch. K. Gupta^a, N. S. Romanovskii<sup>b

a</sup> University of Manitoba
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Let $\mathfrak B$ be a class of groups $A$ which are soluble, equationally Noetherian, and have a central series
$$ A=A_1\geqslant A_2 \geqslant\ldots A_n\geqslant\ldots $$
such that $\bigcap A_n=1$ and all factors $A_n/A_{n+1}$ are torsion-free groups; $D$ is a direct product of finitely many cyclic groups of infinite or prime orders. We prove that the wreath product $D\wr A$ is an equationally Noetherian group. As a consequence we show that free soluble groups of arbitrary derived lengths and ranks are equationally Noetherian.

Keywords: equationally Noetherian group, free soluble group.

UDC: 512.5

Received: 30.05.2006

 English version: Algebra and Logic, 2007, 46:1, 28–36

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