Annali di Matematica Pura ed Applicata

, Volume 192, Issue 6, pp 1043–1057 | Cite as

Prefactorized subgroups in pairwise mutually permutable products

  • A. Ballester-Bolinches
  • J. C. Beidleman
  • H. Heineken
  • M. C. Pedraza-Aguilera
Article
  • 126 Downloads

Abstract

We continue here our study of pairwise mutually and pairwise totally permutable products. We are looking for subgroups of the product in which the given factorization induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized Carter subgroup and a prefactorized system normalizer exist. A less stringent property have \({\mathcal {F}}\) -residual, \({\mathcal F}\) -projector and \({\mathcal {F}}\) -normalizer for any saturated formation \({\mathcal {F}}\) including the supersoluble groups.

Keywords

Finite group Permutability Factorization Saturated formation 

Mathematics Subject Classification (2000)

20D10 20D20 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2012

Authors and Affiliations

  • A. Ballester-Bolinches
    • 1
  • J. C. Beidleman
    • 2
  • H. Heineken
    • 3
  • M. C. Pedraza-Aguilera
    • 4
  1. 1.Departament d’ÀlgebraUniversitat de ValènciaBurjassot, ValènciaSpain
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA
  3. 3.Institut für MathematikUniversität Würzburg Am HublandWürzburgGermany
  4. 4.Instituto Universitario de Matemática Pura y AplicadaUniversidad Politécnica de ValenciaValenciaSpain

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