Finite groups with permutable complete Wielandt sets of subgroups

Let W be a set of nilpotent Hall subgroups of a finite group G. We say that W is a Wielandt set if for each prime p dividing vertical bar G vertical bar there is exactly one subgroup W is an element of W such that p divides vertical bar W vertical bar. In this paper, we study the influence of Wielandt sets on the structure of G. In particular, we give conditions under which a normal subgroup of a finite group is hypercyclically embedded.