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In this paper we give necessary conditions on group presentations, with twogenerators 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 $2$-bridge virtualknot. Moreover, we present a combinatorial proof of the fact that these groupsare not $2$-bridge classical knot groups.

Some Baumslag-Solitar groups are two bridges virtual knots