Varieties of Exponential MR-Groups

Abstract—The concepts of a variety of exponential MR-groups and tensor completions of groups in varieties are introduced. The relationships between free groups of a given variety under different rings of scalars are studied, and varieties of abelian MR-groups are described. Moreover, several analogues of n-class nilpotent groups are considered and compared in the category of MR-groups. It is shown that the completion of a 2‑class nilpotent MR-group is 2-class nilpotent.