The total system can be antisymmetrized by the total antisymmetrizer A A B which consists of the (N A + N B)! terms in the group S N A + N B. However, in this way one does not take advantage of the partial antisymmetry that is already present. It is more economic to use the fact that the product of the two subgroups is also a subgroup, and to consider the left cosets of this product group in S N A + N B :