Geodesic
On the classification of varieties generated by wreath products of groups
Izvestiya. Mathematics , Tome 82 (2018) no. 5, pp. 1006-1018

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We propose a classification of all cases when, for a nilpotent group $A$ of finite exponent and an abelian group $B$, the variety $\operatorname{var}(A \mathbin{\mathrm{Wr}} B)$ generated by their wreath product is equal to the product $\operatorname{var}(A)\operatorname{var}(B)$ of the varieties $\operatorname{var}(A)$ and $\operatorname{var}(B)$ generated by $A$ and $B$. This generalizes some results in the literature concerning the same problem for more restricted types of groups. This classification extends our earlier work on varieties generated by wreath products of abelian groups and wreath products of finite groups.
Keywords: wreath products of groups, varieties of groups, products of varieties, abelian and nilpotent groups, critical groups. 
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     author = {V. H. Mikaelian},
     title = {On the classification of varieties generated by wreath products of groups},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a5/}
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V. H. Mikaelian. On the classification of varieties generated by wreath products of groups. Izvestiya. Mathematics , Tome 82 (2018) no. 5, pp. 1006-1018. http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a5/