Groups sharing some varietal properties with supersoluble groups

Abstract

AbstractIn this note a formation U is considered which can be defined by a sequence of laws which ‘almost’ hold in every finite supersoluble group. The class U contains all finite supersoluble groups and each group in U has a Sylow tower.It is shown that a finite group belongs to U if and only if all of its subgroups with nilpotent commutator subgroup are supersoluble. A more general result concerning classes of this type finally proves that U is a saturated formation.