Some reducibility properties for pseudovarieties of the form DRH

Abstract

ABSTRACTLet 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∨W, and V W.