Geodesic
Varieties of exponential $MR$-groups
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 5-8

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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.
Keywords: Lyndon $R$-groups, $MR$-groups, variety of $MR$-groups, $\alpha$-commutator, $R$-commutant, tensor completion, nilpotent $MR$-group. 
@article{DANMA_2020_490_a0,
     author = {M. G. Amaglobeli},
     title = {Varieties of exponential $MR$-groups},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {5--8},
     publisher = {mathdoc},
     volume = {490},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_490_a0/}
}
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M. G. Amaglobeli. Varieties of exponential $MR$-groups. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 5-8. http://geodesic.mathdoc.fr/item/DANMA_2020_490_a0/