ALGEBRAIC THEORY OF RAY REPRESENTATIONS OF FINITE GROUPS

A theory of characters of ray representations of finite groups, that does not use any reference to a covering group, is derived by defining two generalizations of the concept of a group's class. Orthogonality relations are obtained over one of these generalized classes. This theory is used to discuss subduction and induction of ray representations while the Frobenius reciprocity theorem and generalizations thereof are proved. The theory provides a more efficient method of deriving and treating ray representations of finite groups for a given factor system than has previously been made available.