Criterions of supersolubility of some finite factorizable groups

Let A, B be subgroups of a group G and theta not equal X subset of G. A subgroup A is said to be X-permutable with B if for some x is an element of X we have AB(x) = B-x A [1].obtain some new criterions for supersolubility of a finite group G = AB, where A and B are supersoluble groups. In particular, we prove that a finite group G = AB is supersoluble provided A, B are supersolube subgroups of G such that every primary cyclic su of A X-permutes with if every Sylow subgroup of B and return every primary cyclic Sylow subgroup of B X-permutes with every subgroup of A where X = F(G) is the Fitting subgroup of G.