G-covering systems of subgroups for the class of supersoluble 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 wherever either Sigma = empty set or Sigma not equal empty set and every subgroup in Sigma belongs to F. In this paper, we provide some nontrivial sets of subgroups of a finite group G which are G-covering subgroup systems for the class of supersoluble groups. These are the generalizations of some recent results, such as in [1-3].