Computing relative abelian kernels of finite monoids

Let be a pseudovariety of abelian groups corresponding to a recursive supernatural number. In this note we explain how a concrete implementation of an algorithm to compute the kernel of a finite monoid relative to can be achieved. The case of the pseudovariety of all finite abelian groups was already treated by the second author and plays an important role here, where we will be interested in the proper subpseudovarieties of . Our work relies on an algorithm obtained by Steinberg.