Product varieties of m-groups
Tóm tắt
A new concept of mimicking is introduced. We point out representations that mimic a variety
$$ \mathcal{A} $$
of Abelian m-groups and a variety
$$ \mathcal{J} $$
of m-groups defined by an identity x* = x-1. It is proved that if a variety
$$ \mathcal{U} $$
of m-groups is generated by some class of m-groups, and a variety
$$ \mathcal{V} $$
of m-groups is mimicked by some class of m-groups, then their product
$$ \mathcal{U}\cdot \mathcal{V} $$
is generated by wreath products of groups in the respective classes. For every natural n, we construct m-groups generating varieties
$$ {{\mathcal{J}}^n}=\left( {{{\mathcal{J}}^{n-1 }}} \right)\cdot \mathcal{J} $$
and
$$ {{\mathcal{A}}^n}=\left( {{{\mathcal{A}}^{n-1 }}} \right)\cdot \mathcal{A} $$
.
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