  Symmetries of spacetimes with null dust field as a source compatible with
asymptotic flatness are studied by using the Bondi-Sachs-van der Burg
formalism. It is shown that in an axially symmetric spacetime with null dust
field in which at least locally a smooth null infinity in the sense of Penrose
exists, the only allowable additional Killing vector forming with the axial one
a two-dimensional Lie algebra (the axial and the additional Killing vector are
not assumed to be hypersurface orthogonal) is a supertranslational Killing
vector and the gravitational field is then non-radiative (the Weyl tensor has a
non-radiative character).
