SU(m n⊇SU(m)×SU(n) isoscalar factors and S(f1+f2)⊇S( f1)×S( f2) isoscalar factors

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Abstract
A simple relation is found between the isoscalar factor (ISF) of the unitary group and those of the permutation group, i.e. the SU(mn)⊆SU(m)×SU(n)ISF is equal to the S( f1+f2)⊆S( f1)×S( f2) ISF. Since the values of S( f1+f2)⊆S( f1)×S( f2)ISF are independent of m and n, one arrives at an important conclusion that the values of SU(mn)⊆SU(m)×SU(n) ISF are also independent of m and n. Therefore they can be calculated for all m and n by a single stroke instead of one m and one n at a time. An eigenfunction metho for evaluating the SU(mn)⊆SU(m)×SU(n)ISF is given which can be easily translated into a computer program.