Abstract
In this paper, we give sufficient conditions on group presentations, with two generators and one relator, in order to be the group of a virtual knot diagram. Although those conditions are not enough, we use them to determine, completely, whether or not a Baumslag–Solitar group is the group of a two-bridge virtual knot. Moreover, we present a combinatorial proof of the fact that these groups are not two-bridge classical knot groups.
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