A decomposition theorem for G-groups

Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups (G-groups). In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible.