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A group-theoretical method, via Wada's representations, is presented todistinguish Kishino's virtual knot from the unknot. Biquandles are constructedfor any group using Wada's braid group representations. Cocycle invariants forthese biquandles are studied. These invariants are applied to show thenon-existence of Alexander numberings and checkerboard colorings.

VIRTUAL KNOT INVARIANTS FROM GROUP BIQUANDLES AND THEIR COCYCLES