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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)
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Abstract

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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 

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