The introduction of a non-abelian gauge group embedded into the rigid symmetry group G of a field theory with abelian vector fields and no corresponding charges, requires in general the presence of a hierarchy of p-form gauge fields. The full gauge algebra of this hierarchy can be defined independently of a specific theory and is encoded in the embedding tensor that encodes the gauge group. When applied to specific Lagrangians, the algebra is deformed in an intricate way and in general will only close up to equations of motion. The group-theoretical structure of the hierarchy exhibits many interesting features, which have been studied starting from the low-p forms. Here the question is addressed what happens generically for high values of p. In addition a number of other features is discussed concerning the role that the p-forms play in various deformations of the theory.