  The aim of this paper is to clarify the role of the nilpotent fermionic
generator Q' introduced in Ref. [3] and appearing in the hidden supergroup
underlying the free differential algebra (FDA) of D=11 supergravity. We give a
physical explanation of its role by looking at the gauge properties of the
theory. We find that its presence is necessary, in order that the extra 1-forms
of the hidden supergroup give rise to the correct gauge transformations of the
p-forms of the FDA.
  This interpretation is actually valid for any supergravity containing
antisymmetric tensor fields, and any supersymmetric FDA can always be traded
for a hidden Lie superalgebra containing extra fermionic nilpotent generators.
As an interesting example we construct the hidden superalgebra associated with
the FDA of N=2, D=7 supergravity. In this case we are able to parametrize the
mutually non local 2- and 3-form B^(2) and B^(3) in terms of hidden 1-forms and
find that supersymmetry and gauge invariance require in general the presence of
two nilpotent fermionic generators in the hidden algebra. We propose that our
approach, where all the invariances of the FDA are expressed as Lie derivatives
of the $p$-forms in the hidden supergroup manifold, could be an appropriate
framework to discuss theories defined in enlarged versions of superspace
recently considered in the literature, such us double field theory and its
generalizations.
