  We denote by kappa the implicit signature that contains the multiplication
and the (omega-1)-power. It is proved that for any completely kappa-reducible
pseudovariety of groups H, the pseudovariety DRH of all finite semigroups whose
regular R-classes are groups in H is completely kappa-reducible as well. The
converse also holds. The tools used by Almeida, Costa, and Zeitoun for proving
that the pseudovariety of all finite R-trivial monoids is completely
kappa-reducible are adapted for the general setting of a pseudovariety of the
form DRH.
