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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - M. G. Amaglobeli
TI  - Varieties of exponential $MR$-groups
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 5
EP  - 8
VL  - 490
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_490_a0/
LA  - ru
ID  - DANMA_2020_490_a0
ER  - 
%0 Journal Article
%A M. G. Amaglobeli
%T Varieties of exponential $MR$-groups
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 5-8
%V 490
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2020_490_a0/
%G ru
%F DANMA_2020_490_a0
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/

[1] Lyndon R.C., Trans. Amer. Math. Soc., 96 (1960), 518–533 | DOI | MR | Zbl

[2] Myasnikov A.G., Remeslennikov V.N., Sib. mat. zhurn., 35:5 (1994), 1106–1118 | MR | Zbl

[3] Amaglobeli M.G., Remeslennikov V.N., DAN, 443:4 (2012), 410–413 | Zbl

[4] Amaglobeli M.G., Algebra i logika, 57:2 (2018), 137–148 | MR | Zbl

[5] Myasnikov A.G., Remeslennikov V.N., Intern. J. Algebra Comput., 1996, no. 6, 687–711 | DOI | MR | Zbl

[6] Baumslag G., Myasnikov A., Remeslennikov V., Geom. Dedicata, 92 (2002), 115–143 | DOI | MR | Zbl

[7] Amaglobeli M.G., Remeslennikov V.N., Sib. matem. zhurn., 54:1 (2013), 8–19 | MR | Zbl

[8] Amaglobeli M., Remeslennikov V., Georgian Math. J., 22:4 (2015), 441–449 | DOI | MR | Zbl

[9] Amaglobeli M.G., DAN, 486:2 (2019), 147–150 | Zbl

[10] Gorbunov V.A., Algebraicheskaya teoriya kvazimnogoobrazii, Nauch. kniga, Novosibirsk, 1999