A formal power series attached to a class function on a group and its application to the characterisation of characters

In Frobenius' initial papers on group characters he introduced k-characters in order to give an algorithm to calculate the irreducible factors of the group determinant. We show how his work leads naturally to the construction of a formal power series for any class function on a group, which terminates if and only if the class function is a character. This is then used to obtain a criterion for a class function to be a character.