REPRESENTATIONS AND CLASSES IN GROUPS OF FINITE ORDER

There are two main results in this paper. First, it is shown that we can develop a theory of classes in close analogy to the usual theory of representations. We can introduce concepts, such as reducible and irreducible classes, sum and product of classes, reduction of a class when going from a group to a subgroup, etc. Second, it is shown that it is possible to associate a magic square" to each group. It is related to the numbers of pain of commuting elements between classes and it can be used immediately to find the structure of the "tensor operators" of the group."