Abstract
The authors have previously constructed two representations of the virtual braid group into the automorphism group of the free product of a free group and a free abelian group. Using them, we construct the two groups, each of which is a virtual link invariant. By the example of the virtual trefoil knot we show that the constructed groups are not isomorphic, and establish a connection between these groups as well as their connection with the group of the virtual trefoil knot which was defined by Carter, Silver, and Williams.
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Original Russian Text Copyright © 2017 Bardakov V.G., Mikhalchishina Yu.A., and Neshchadim M.V.
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 5, pp. 989–1003, September–October, 2017; DOI: 10.17377/smzh.2017.58.503.
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Bardakov, V.G., Mikhalchishina, Y.A. & Neshchadim, M.V. Virtual link groups. Sib Math J 58, 765–777 (2017). https://doi.org/10.1134/S0037446617050032
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DOI: https://doi.org/10.1134/S0037446617050032