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For a group $ G $ we consider its tensor square $G \otimes G$ and exteriorsquare $G \wedge G$. We prove that for a circularly orderable group $G$, undersome assumptions on $H_1(G)$ and $H_2(G)$, its exterior square and tensorsquare are left-orderable. This yields an obstruction for a circularlyorderable group $G$ to have torsion. We apply these results to study circularorderability of tabulated virtual knot groups.

Non-abelian tensor product and circular orderability of groups