Semidirect products with the pseudovariety of all finite groups

摘要

This is a survey of recent results related to semidirect products of an arbitrary pseudovariety with the pseudovariety of all finite groups. The main flavour is the establishment of links between various operators on pseudovarieties, some obviously computable, others known not to be so. This not only leads to decidability results but does so in a sort of uniform way which has a structural tint even though the arguments are mostly syntactical.