Amaglobeli, M. G. Exponential \(MR\)-groups: faithful \(R\)-completion. (English. Russian original) Zbl 1481.20194 Dokl. Math. 99, No. 3, 263-265 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 486, No. 2, 147-150 (2019). Summary: This paper is devoted to partial exponential \(MR\)-groups that are isomorphically embeddable in their tensor \(R\)-completions. As a consequence, the free \(MR\)-groups and free \(MR\)-products are described in terms of usual group-theoretical free constructions. Cited in 1 Document MSC: 20J15 Category of groups 20B07 General theory for infinite permutation groups 20E05 Free nonabelian groups PDFBibTeX XMLCite \textit{M. G. Amaglobeli}, Dokl. Math. 99, No. 3, 263--265 (2019; Zbl 1481.20194); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 486, No. 2, 147--150 (2019) Full Text: DOI References: [1] Lyndon, R. C., No article title, Trans. Amer. Math. Soc., 96, 518-533 (1960) · Zbl 0108.02501 · doi:10.1090/S0002-9947-1960-0151502-6 [2] Myasnikov, A. G.; Remeslennikov, V. N., No article title, Sib. Math. J., 35, 1106-1118 (1994) · Zbl 0851.20050 · doi:10.1007/BF02104576 [3] Amaglobeli, M. G.; Remeslennikov, V. N., No article title, Dokl. Math., 443, 410-413 (2012) [4] Myasnikov, V. N.; Remeslennikov, V. N., No article title, Int. J. Algebra Comput., 6, 687-711 (1996) · Zbl 0866.20014 · doi:10.1142/S0218196796000398 [5] Baumslag, G.; Myasnikov, A.; Remeslennikov, V., No article title, Geom. Dedicata, 92, 115-143 (2002) · Zbl 1011.20041 · doi:10.1023/A:1019687202544 [6] Amaglobeli, M. G.; Remeslennikov, V. N., No article title, Sib. Math. J., 54, 8-19 (2013) · Zbl 1300.20050 [7] Amaglobeli, M.; Remeslennikov, V., No article title, Georgian Math. J., 22, 441-449 (2015) · Zbl 1361.20004 · doi:10.1515/gmj-2015-0046 [8] Amaglobeli, M. G.; Remeslennikov, V. N., No article title, Sib. Math. J., 57, 1107-1207 (2016) · Zbl 1393.20011 · doi:10.1134/S003744661606001X [9] Amaglobeli, M. G., No article title, Algebra Logika, 57, 137-149 (2018) · Zbl 1485.20072 · doi:10.1007/s10469-018-9482-9 [10] Baumslag, G.; Illinois, J., No article title, Math., 30, 235-245 (1986) · Zbl 0592.20049 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.