  Let H be a pseudovariety of groups and DRH be the pseudovariety containing
all finite semigroups whose regular R-classes belong to H. We study the
relationship between reducibility of H and of DRH with respect to several
particular classes of systems of equations. The classes of systems considered
(of pointlike, idempotent pointlike and graph equations) are known to play a
role in decidability questions concerning pseudovarieties of the forms V * W, V
join W, and V malcev W.
