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The equation [x, y] = g in partially commutative groups

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Abstract

A partially commutative group is a group defined by generators and relations so that all defining relations are of the form: the commutators of some pairs of generators equal the identity element. We consider an algorithm for checking whether a given element of the group is a commutator, generalizing Wicks’s theorem for free groups.

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Authors and Affiliations

  1. Vologda State Pedagogical University, Vologda

    S. L. Shestakov

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  1. S. L. Shestakov
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Original Russian Text Copyright © 2005 Shestakov S. L.

Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Zhurnal, Vol. 46, No. 2, pp. 466–477, March–April, 2005.

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Shestakov, S.L. The equation [x, y] = g in partially commutative groups. Sib Math J 46, 364–372 (2005). https://doi.org/10.1007/s11202-005-0038-6

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  • DOI: https://doi.org/10.1007/s11202-005-0038-6

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