Supersoluble conditions and transfer control

In this paper we give a new condition for a Sylow p-subgroup of a finite group to control transfer. Then it is deduced a characterization of supersoluble group that can be seen as a generalization of the well konwn result concerning the supersolubility of finite groups with cyclic Sylow subgroups. Moreover a condition for a normal embedding of a strongly closed p-subgroup is given These results make use of the properties of G-chain and Phi-chain.