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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 4, Pages 902–913 (Mi smj2465)  
This article is cited in 2 scientific papers (total in 2 papers)

Quasivarieties generated by partially commutative groups

E. I. Timoshenko

Novosibirsk State Technical University, Novosibirsk, Russia
Full-text PDF (329 kB) Citations (2)
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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.
Received: 03.07.2012
English version:
Siberian Mathematical Journal, 2013, Volume 54, Issue 4, Pages 722–730
DOI: https://doi.org/10.1134/S0037446613040125
Bibliographic databases:
Document Type: Article
UDC: 512.5
Language: Russian
Citation: E. I. Timoshenko, “Quasivarieties generated by partially commutative groups”, Sibirsk. Mat. Zh., 54:4 (2013), 902–913; Siberian Math. J., 54:4 (2013), 722–730
Citation in format AMSBIB
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\paper Quasivarieties generated by partially commutative groups
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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