Geodesic
Category of $\mathrm{MR}$-groups over a ring $\mathrm R$
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 2, pp. 12-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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The category of exponential $\mathrm{MR}$-groups for an associative ring $\mathrm R$ with unity is defined in [1]. The present paper is devoted to the study of partial exponential $\mathrm{MR}$-groups which are isomorphically embedded in their tensor completion over the ring $\mathrm R$. The key to its understanding is the notion of tensor completion introduced in [1]. As a consequence, the description of free $\mathrm{MR}$-groups in the language of group constructions is obtained. 
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     title = {Category of $\mathrm{MR}$-groups over a~ring~$\mathrm R$},
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M. G. Amaglobeli. Category of $\mathrm{MR}$-groups over a ring $\mathrm R$. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 2, pp. 12-18. http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a1/

[1] Myasnikov A. G., Remeslennikov V. N., “Stepennye gruppy. I. Osnovy teorii i tenzornye popolneniya”, Sib. mat. zhurn., 35:5 (1994), 1106–1118 | MR | Zbl

[2] Lyndon R. C., “Groups with parametric exponents”, Trans. Amer. Math. Soc., 96 (1960), 518–533 | DOI | MR | Zbl

[3] Baumslag G., “Free abelian $X$-groups”, Illinois J. Math., 30:2 (1986), 235–245 | MR | Zbl

[4] Hall Ph., The Edmonton Notes on Nilpotent Groups, Queen Mary College Math. Notes. Mathematics Department, Queen Mary College, London, 1969, iii+76 pp. | MR

[5] Myasnikov A. G., Remeslennikov V. N., “Exponential groups. II. Extensions of centralizers and tensor completion of CSA-groups”, Internat. J. Algebra Comput., 6:6 (1996), 687–711 | DOI | MR | Zbl

[6] Baumslag G., Myasnikov A., Remeslennikov V., “Discriminating completions of hyperbolic groups”, Dedicated to John Stallings on the occasion of his 65th birthday, Geom. Dedicata, 92 (2002), 115–143 | DOI | MR | Zbl

[7] Amaglobeli M. G., “On the permutability of a functor of tensor completion with principal group operations”, Appl. Math. Inform. Mech., 15:1 (2010), 3–10 | MR

[8] Amaglobeli M., Bokelavadze T., “Abelian and nilpotent varieties of power groups”, Georgian Math. J., 18:3 (2011), 425–439 | MR | Zbl

[9] Amaglobeli M., “Power groups”, J. Math. Sci., 186:6 (2012), 811–865 | DOI | MR | Zbl

[10] Amaglobeli M. G., Remeslennikov V. N., “Svobodnye 2-stupenno nilpotentnye $\mathrm R$-gruppy”, Dokl. AN, 443:4 (2012), 410–413 | MR | Zbl

[11] Amaglobeli M. G., Remeslennikov V. N., “Rasshireniya tsentralizatorov v nilpotentnykh gruppakh”, Sib. mat. zhurn., 54:1 (2013), 8–19 | MR

[12] Baumslag G., “On free $\mathcal D$-groups”, Comm. Pure Appl. Math., 18 (1965), 25–30 | DOI | MR | Zbl

[13] Polin S. V., “Svobodnye razlozheniya v mnogoobraziyakh $\lambda$-grupp”, Mat. sb., 87(129):3 (1972), 377–395 | MR | Zbl