Power pseudovarieties of semigroups. II (Q1073187)

[See also the preceding review.] If V is a permutative pseudovariety, i.e. every member of V satisfies some permutative identity \(x_ 1...x_ pyzx_{p+1}...x_ m=x_ 1...x_ pzyx_{p+1}...x_ m\), then \(P^ 2V\) and \(P'{}^ 2V\) can be characterized. If V is not permutative then \(P'{}^ 3V=S\). The results render a presentation of the semigroup of operators generated by P and P' which turns out to be finite.