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 characteri-zation of supersoluble groups that can be seen as a generalization of the well known 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-chains and \Phi-chains‎. 

Keywords:

transfer control , normal p-complement , supersoluble groups , strongly closed subgroup