Article contents
Groups sharing some varietal properties with supersoluble groups
Published online by Cambridge University Press: 09 April 2009
Abstract
In 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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1983
References
- 3
- Cited by