On supplements of subgroups of finite groups
- Xianhua Li
- Adolfo Ballester-Bolinches
ISSN: 0392-4041
Year of publication: 2006
Volume: 9
Issue: 3
Pages: 567-574
Type: Article
More publications in: Bollettino dell unione matematica italiana. Sezione B: articoli di ricerca matematica
Abstract
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.