Supersoluble conditions and transfer control

Document Type: Ischia Group Theory 2012

Authors

1 Universita Bologna

2 Dipartimento di Matematica U. Dini Viale Morgagni 67/A 50134 FIRENZE

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.
 

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