Supersoluble conditions and transfer control

Abstract

‎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.