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A question from the Kourovka notebook on formation products

Published online by Cambridge University Press:  17 April 2009

A. Ballester-Bolinches
Affiliation:
Departament d'Àlgebra, Universitat de València, Dr. Moliner, 50, E-46100 Burjassot, València, Spain, e-mail: Adolfo.Ballester@uv.es, clacalo@alumni.uv.es
Clara Calvo
Affiliation:
Departament d'Àlgebra, Universitat de València, Dr. Moliner, 50, E-46100 Burjassot, València, Spain, e-mail: Adolfo.Ballester@uv.es, clacalo@alumni.uv.es
R. Esteban-Romero
Affiliation:
Departament de Matemàtica Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, E-46022 València, Spain, e-mail: resteban@mat.upv.es
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Abstract

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It is shown in this paper that if  is a class of simple groups such that π() = char , the -saturated formation ℌ generated by a finite group cannot be expressed as the Gaschütz product  ∘  of two non--saturated formations if ℌ ≠ . It answers some open questions on products of formations. The relation between ω-saturated and -saturated formations is also discussed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Ballester-Bolinches, A., Calvo, C. and Esteban-Romero, R., ‘On -saturated formations of finite groups’, preprint.Google Scholar
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