Myasnikov, A. G.; Romanovskii, N. S. Logical aspects of the theory of divisible rigid groups. (English. Russian original) Zbl 1319.20032 Dokl. Math. 90, No. 3, 697-698 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 459, No. 2, 154-155 (2014). Announcement of results. Cited in 10 Documents MSC: 20F16 Solvable groups, supersolvable groups 20F14 Derived series, central series, and generalizations for groups 03C60 Model-theoretic algebra 20A15 Applications of logic to group theory 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 20E07 Subgroup theorems; subgroup growth 20E22 Extensions, wreath products, and other compositions of groups 14A22 Noncommutative algebraic geometry 20F70 Algebraic geometry over groups; equations over groups 20C07 Group rings of infinite groups and their modules (group-theoretic aspects) Keywords:rigid solvable groups; universal theories of groups; decidable theories; recursive systems of universal axioms; existential axioms; universal equivalences; decidability PDF BibTeX XML Cite \textit{A. G. Myasnikov} and \textit{N. S. Romanovskii}, Dokl. Math. 90, No. 3, 697--698 (2014; Zbl 1319.20032); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 459, No. 2, 154--155 (2014) Full Text: DOI References: [1] Myasnikov, A; Romanovskiy, N, No article title, J. Algebra, 324, 2814-2831, (2010) · Zbl 1234.20052 [2] Romanovskii, N S, No article title, Algebra Logic, 47, 426-434, (2008) · Zbl 1245.20035 [3] Romanovskii, N S, No article title, Algebra Logic, 48, 147-160, (2009) · Zbl 1245.20036 [4] Myasnikov, A G; Romanovskii, N S, No article title, Algebra Logic, 50, 539-552, (2011) · Zbl 1263.20034 [5] Gupta, Ch K; Romanovskii, N S, No article title, Algebra Logic, 46, 28-36, (2007) · Zbl 1156.20032 [6] Romanovskii, N S, No article title, Algebra Logic, 48, 449-464, (2009) · Zbl 1245.20054 [7] Romanovskii, N S, No article title, Algebra Logic, 49, 539-550, (2010) · Zbl 1236.20039 [8] Mal’tsev, A I, No article title, Dokl. Akad. Nauk SSSR, 130, 495-498, (1960) [9] Romanovskii, N S, No article title, Algebra Logic, 51, 259-263, (2012) · Zbl 1267.20052 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.