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This article is cited in 1 scientific paper (total in 1 paper) Quasivarieties generated by partially commutative groups E. I. Timoshenko Novosibirsk State Technical University, Novosibirsk, Russia Abstract: We prove that a partially commutative metabelian group is a subgroup in a direct product of torsion-free abelian groups and metabelian products of torsion-free abelian groups. From this we deduce that all partially commutative metabelian (nonabelian) groups generate the same quasivariety and prevariety. On the contrary, there exists an infinite chain of different quasivarieties generated by partially commutative groups with defining graphs of diameter 2. Keywords: quasivariety, prevariety, partially commutative group, metabelian group, graph.  Full text:
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English version: Siberian Mathematical Journal, 2013, 54:4,  Bibliographic databases:   
UDC: 512.5 Received: 03.07.2012 Citation: E. I. Timoshenko, “Quasivarieties generated by partially commutative groups”, Sibirsk. Mat. Zh., 54:4 (2013), 
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