G-covering systems of subgroups for classes of p-supersoluble and p-nilpotent finite groups

Let F be a class of groups. Given a group G, assign to G some set of its subgroups Sigma = Sigma(G). We say that Sigma is a G-covering system of subgroups for F (or, in other words, an F-covering system of subgroups in G) if G is an element of F whenever either Sigma = circle divide or Sigma not equal circle divide and every subgroup in Sigma belongs to F. We find the systems of subgroups in the class of finite soluble groups G which are simultaneously the G-covering systems of subgroups for the classes of p-supersoluble and p-nilpotent groups.