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14.26 (1999)

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A quasivariety $\mathfrak{M}$ is closed under direct $\mathbb{Z}$-wreath products if the direct wreath product $G \wr \mathbb{Z}$ belongs to $\mathfrak{M}$ for every $G \in \mathfrak{M}$ (here $\mathbb{Z}$ is an infinite cyclic group). Is the quasivariety generated by the class of all nilpotent torsion-free groups closed under direct $\mathbb{Z}$-wreath products?

Contributor: A. I. Budkin

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