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.
@article{IM2_2018_82_5_a5,
author = {V. H. Mikaelian},
title = {On the classification of varieties generated by wreath products of groups},
journal = {Izvestiya. Mathematics },
pages = {1006--1018},
publisher = {mathdoc},
volume = {82},
number = {5},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a5/}
}
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/