  In the context of Teleparallel Equivalent of General Relativity - TEGR - we
have obtained, through the second kind gauge transformations, the most
fundamental transformations, namely, the first kind ones. We show that
considering the possibility of decomposing the components of the tetrad field
as a trivial part plus some potential besides the usual translational and
Lorentz potentials, there is also the possibility that the symmetry group of
internal space be a generalization of the Poincar\'e group. Still in the
analysis of transformations in the internal space, we saw that for the case in
which the decomposition of the tetrad field components includes only a trivial
part plus a translational potential, we are able to recover just the
translational group. Moreover, the internal space of gravity must be the very
physical space - on a local scale - in such a way that the gauge symmetry group
is the kinematical group of the physical space itself. This group was obtained,
and seems to generalize the Poincar\'e group.
