# 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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The orbits for the operation on V are briefly demonstrated.

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