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    the orbits for the operation on V

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    The symmetric group Sâ?? operates on two sets U and V of order 3. Decompose the product set UÃ?V into orbits for the diagonal action g(u,v)=(gu,gv), when

    a) the operations on U and V are transitive,
    b) the operation on U is transitive, the orbits for the operation on V are {vâ?} and {vâ??,vâ??}.

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    Solution Summary

    The orbits for the operation on V are briefly demonstrated.