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Groups whose primary subgroups are normal sensitive

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Abstract

A subgroup \(H\) of a group \(G\) is said to be normal sensitive in \(G\) if for every normal subgroup \(N\) of \(H, N=H\cap N^{G}\). In this paper we study locally finite groups whose \(p\)-subgroups are normal sensitive. We show the connection between these groups and groups in which Sylow permutability is transitive.

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Acknowledgments

This research was supported by Proyecto MTM2010-19938-C03-01 (Ballester-Bolinches, Pedraza) and Proyecto MTM2010-19938-C03-03 (Kurdachenko, Otal) from MINECO (Spain). The third author was also supported by Gobierno of Aragón (Spain) and FEDER funds.

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Authors and Affiliations

  1. Departament d’Àlgebra, Universitat de València, Dr Moliner 50, 46100 , Burjassot (València), Spain

    Adolfo Ballester-Bolinches

  2. Department of Algebra, National University of Dnepropetrovsk, Gagarin prospect 72, 49010 , Dnepropetrovsk, Ukraine

    Leonid A. Kurdachenko

  3. Departmento de Matemáticas, IUMA, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 , Zaragoza, Spain

    Javier Otal

  4. Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 , Valencia, Spain

    Tatiana Pedraza

Authors
  1. Adolfo Ballester-Bolinches
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  2. Leonid A. Kurdachenko
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  3. Javier Otal
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  4. Tatiana Pedraza
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Corresponding author

Correspondence to Javier Otal.

Additional information

Communicated by J. S. Wilson.

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Ballester-Bolinches, A., Kurdachenko, L.A., Otal, J. et al. Groups whose primary subgroups are normal sensitive. Monatsh Math 175, 175–185 (2014). https://doi.org/10.1007/s00605-013-0566-2

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  • DOI: https://doi.org/10.1007/s00605-013-0566-2

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