Remarks on chains of weakly closed subgroups.

In this paper we generalize and unify several results proved in recent papers about the existence of normal p-complements and conditions on supersolubility. Moreover a counterexample is given to a question in [Guo and Wei, J. Group Theory 13: 267-276, 2010] and it is proved that a finite group is 2-nilpotent if the cyclic subgroups of order less or equal than four are strongly closed. [ABSTRACT FROM AUTHOR]