On supplements of subgroups of finite groups
- Xianhua Li
- Adolfo Ballester-Bolinches
ISSN: 0392-4041
Any de publicació: 2006
Volum: 9
Número: 3
Pàgines: 567-574
Tipus: Article
Altres publicacions en: Bollettino dell unione matematica italiana. Sezione B: articoli di ricerca matematica
Resum
In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubi- lity, supersolvability and nilpotence of a finite group are given.