Product varieties of m-groups

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