A Decomposition Theorem for Group Representations

In this paper we establish a decomposition theorem for an ordinary representation of a finite group G in any category C{\mathcal C} which expresses a suitable irreducible representation of G as the tensor product of two projective ones. The celebrated theorem due to Clifford for a linear representation turns out to be a particular case of it. For that purpose, a definition of projective extension of an ordinary representation of a normal subgroup of G is introduced, as well as a tensor product between two of them.