Abstract
The most important theorem that connects induced and subduced representations, is the Frobenius reciprocity theorem. If the factor systems of a group are classified according to p-equivalence, it can be shown that there is a finite number of such classes. Any two of these classes can be multiplied to give a third class by multiplying one factor system from the first with one from the second and defining the third class to be the class containing the product of the two factor systems. It can then be shown that with this kind of multiplication the classes of factor systems form a finite abelian group. This group is called the multiplicator of the original group. The spin representations of the 3-dimensional rotation group can be considered as projective representations.
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