  We consider non-rotating geodesic perfect fluid spacetimes which are purely
radiative in the sense that the gravitational field satisfies the covariant
transverse conditions div H = div E = 0. We show that when the shear tensor S
is degenerate, H, E and S necessarily commute and hence the resulting
spacetimes are hypersurface homogeneous of Bianchi class A (modulo some purely
electric exceptions).
