Bloshchitsyn, V. Ya.; Timoshenko, E. I. Comparison between the universal theories of partially commutative metabelian groups. (English. Russian original) Zbl 1400.20021 Sib. Math. J. 58, No. 3, 382-391 (2017); translation from Sib. Mat. Zh. 58, No. 3, 497-509 (2017). Summary: We find necessary and sufficient conditions for the coincidence of the universal theories of partially commutative groups of metabelian varieties defined by acyclic graphs. Cited in 2 Documents MSC: 20F05 Generators, relations, and presentations of groups 20E10 Quasivarieties and varieties of groups 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 20F70 Algebraic geometry over groups; equations over groups 03B10 Classical first-order logic 03C60 Model-theoretic algebra 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) Keywords:metabelian group; partially commutative group; acyclic graph; universal theory PDFBibTeX XMLCite \textit{V. Ya. Bloshchitsyn} and \textit{E. I. Timoshenko}, Sib. Math. J. 58, No. 3, 382--391 (2017; Zbl 1400.20021); translation from Sib. Mat. Zh. 58, No. 3, 497--509 (2017) Full Text: DOI References: [1] Gupta Ch. K. and Timoshenko E. I., “Partially commutative metabelian groups: centralizers and elementary equivalence,” Algebra and Logic, vol. 48, no. 3, 173-192 (2009). · Zbl 1245.20032 · doi:10.1007/s10469-009-9051-3 [2] Timoshenko E. I., “Universal equivalence of partially commutative metabelian groups,” Algebra and Logic, vol. 49, no. 2, 177-196 (2010). · Zbl 1220.20024 · doi:10.1007/s10469-010-9088-3 [3] Gupta Ch. K. and Timoshenko E. I., “Universal theories for partially commutative metabelian groups,” Algebra and Logic, vol. 50, no. 1, 1-16 (2011). · Zbl 1263.20032 [4] Romanovskiĭ N. S., “On Shmel’kin embeddings for abstract and profinite groups,” Algebra and Logic, vol. 38, no. 5, 326-334 (1999). · Zbl 0943.20020 · doi:10.1007/BF02671749 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.