Varieties of exponential R-groups

In this paper we introduce the notion of a variety of exponential MR-groups and tensor completions of groups in varieties. We study relationships between free groups of a given variety under different rings of scalars and describe varieties of abelian MR-groups. Moreover, in the category of MR-groups, we consider several analogs of n-class nilpotent groups. We got that the completion of a 2-class nilpotent group is a 2-class nilpotent.

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