Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-24T11:28:45.565Z Has data issue: false hasContentIssue false
  • English
  • Français

Triple Factorizations and Supersolubility of Finite Groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  11 June 2015

Adolofo Ballester-Bolinches  and
Luis M. Ezquerro
Adolofo Ballester-Bolinches
Affiliation:
Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, València, Spain, (adolfo.ballester@uv.es)
Luis M. Ezquerro
Affiliation:
Departamento de Matemáticas, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Navarra, Spain, (ezquerro@unavarra.es)
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we analyse the structure of a finite group of minimal order among the finite non-supersoluble groups possessing a triple factorization by supersoluble subgroups of pairwise relatively prime indices. As an application we obtain some sufficient conditions for a triple factorized group by supersoluble subgroups of pairwise relatively prime indices to be supersoluble. Many results appear as consequences of our analysis.

Keywords

finite groupsupersoluble groupfactorization

MSC classification

Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20D40: Products of subgroups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 301 - 309
Copyright
Copyright © Edinburgh Mathematical Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Asaad, M. and Shaalan, A., On supersolvability of finite groups, Arch. Math. 53 (1989), 318–326.Google Scholar
2. BallesterBolinches, A., Esteban-Romero, R. and Asaad, M., Products of finite groups, De Gruyter Expositions in Mathematics, Volume 53 (Walter de Gruyter, Berlin, 2010).CrossRefGoogle Scholar
3. Doerk, K., Minimal nicht überauflösbare Gruppen, Math. Z. 91 (1966), 198–205.Google Scholar
4. Doerk, K. and Hawkes, T., Finite soluble groups, De Gruyter Expositions in Mathematics, Volume 54 (Walter de Gruyter, Berlin, 1992).Google Scholar
5. Flowers, N. and Wakefield, T. P., On a group with three supersolvable subgroups of pairwise relatively prime indices, Arch. Math. 95 (2010), 309–315.Google Scholar
6. Friesen, T. K., Products of normal supersolvable groups, Proc. Am. Math. Soc. 30 (1971), 46–48.Google Scholar
7. Huppert, B., Endliche Gruppen I, Grundlehren der mathematischen Wissenschaften, Volume 134 (Springer, 1967).Google Scholar
8. Kegel, O. H., Zur Struktur mehrfach faktorisierbarer endlicher Gruppen, Math. Z. 87 (1965), 42–48.Google Scholar
9. Wang, K., Finite groups with two supersolvable subgroups of coprime indices, Northeast Math. J. 17 (2001), 219–223.Google Scholar