  We calculate the one-loop twist-3 gluon contribution to the flavor-singlet
structure function g_2(x,Q^2) in polarized deep-inelastic scattering and find
that it is dominated by the contribution of the three-gluon operator with the
lowest anomalous dimension (for each moment N). The similar property was
observed earlier for the nonsinglet distributions, although the reason is in
our case different. The result is encouraging and suggests a simple evolution
pattern of g_2(x,Q^2) in analogy with the conventional description of twist-2
parton distributions.
