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

Some reducibility properties for pseudovarieties of the form DRH