Decomposability of minimal defect branched coverings over the projective plane

In this paper we characterize primitive branched coverings with minimal defect over the projective plane with respect to the properties decomposable and indecomposable. This minimality is achieved when the covering surface is also the projective plane, which corresponds to the last case to be solved. As a consequence, we have extended the family of realisations of branched coverings on the projective plane and established a type of generalisation of results on primitive permutation groups.