Geodesic
The property of being equationally Noetherian for some soluble groups
Algebra i logika, Tome 46 (2007) no. 1, pp. 46-59.

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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. 
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Ch. K. Gupta; N. S. Romanovskii. The property of being equationally Noetherian for some soluble groups. Algebra i logika, Tome 46 (2007) no. 1, pp. 46-59. http://geodesic.mathdoc.fr/item/AL_2007_46_1_a2/

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