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Quasivarieties generated by partially commutative groups

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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.

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Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    E. I. Timoshenko

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  1. E. I. Timoshenko
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Correspondence to E. I. Timoshenko.

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Original Russian Text Copyright © 2013 Timoshenko E.I.

The author was supported by the Russian Foundation for Basic Research (Grant 12-01-00084) and the Ministry for Education and Science of the Russian Federation (Grant 14.B37.21.0359).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 902–913, July–August, 2013.

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Timoshenko, E.I. Quasivarieties generated by partially commutative groups. Sib Math J 54, 722–730 (2013). https://doi.org/10.1134/S0037446613040125

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  • DOI: https://doi.org/10.1134/S0037446613040125

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