Projective G-sets Original Research Article

There are many analogies between permutation representations and linear representations. Nevertheless, no version of projective representations is known in the context of the Burnside ring. In this paper, a decomposition theorem of irreducible G-sets similar to Cliffordʹs one which expresses an irreducible linear representation as a product of two projective representations is obtained. As a consequence, the definition of the induction in the Burnside ring is given through the wreath product of symmetric groups.