Reducibility of pointlike problems

We show that the pointlike and the idempotent pointlike problems are reducible with respect to natural signatures in the following cases: the pseudovariety of all finite semigroups in which the order of every subgroup is a product of elements of a fixed set (pi ) of primes; the pseudovariety of all finite semigroups in which every regular (mathcal J)-class is the product of a rectangular band by a group from a fixed pseudovariety of groups that is reducible for the pointlike problem, respectively graph reducible. Allowing only trivial groups, we obtain (omega )-reducibility of the pointlike and idempotent pointlike problems, respectively for the pseudovarieties of all finite aperiodic semigroups ((mathsf{A})) and of all finite semigroups in which all regular elements are idempotents ((mathsf{DA})).