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- Title
On a class of finite soluble groups.
- Authors
Ballester-Bolinches, Adolfo; Cossey, John; Li, Yangming
- Abstract
The aim of this paper is to study the class of finite groups in which every subgroup is self-normalising in its subnormal closure. It is proved that this class is a subgroup-closed formation of finite soluble groups which is not closed under taking Frattini extensions and whose members can be characterised by means of their Carter subgroups. This leads to new characterisations of finite soluble T-, PT- and PST-groups. Finite groups whose p-subgroups, p a prime, are self-normalising in their subnormal closure are also characterised.
- Subjects
SOLVABLE groups; FRATTINI subgroups; NILPOTENT groups; SYLOW subgroups; HYPOTHESIS
- Publication
Journal of Group Theory, 2018, Vol 21, Issue 5, p839
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2018-0015