Monatshefte für Mathematik

, Volume 175, Issue 2, pp 175–185 | Cite as

Groups whose primary subgroups are normal sensitive

  • Adolfo Ballester-Bolinches
  • Leonid A. Kurdachenko
  • Javier Otal
  • Tatiana Pedraza


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.


Locally finite group Normal sensitivity Primary subgroup PST-group T-group 

Mathematics Subject Classification (2000)

20E07 20E15 20F22 20F50 



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.


  1. 1.
    Baer, R.: Situation der Untergruppen und Struktur der Gruppe. S.-B. Heidelberg Akad. 2, 12–17 (1933)Google Scholar
  2. 2.
    Ballester-Bolinches, A., Esteban-Romero, R.: Sylow permutable subnormal subgroups of finite groups. J. Algebra 251, 727–738 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups. De Gruyter expositions in mathematics. Walter de Gruyter, Berlin (2010)CrossRefGoogle Scholar
  4. 4.
    Ballester-Bolinches, A., Kurdachenko, L.A., Otal, J., Pedraza, T.: Infinite groups with many permutable subgroups. Rev. Mat. Iberoamericana 24, 745–764 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bauman, S.: The intersection map of subgroups. Arch. Math. (Basel) 25, 337–340 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Beidleman, J.C., Ragland, M.F.: The intersection map of subgroups and certain classes of finite groups. Ric. Mat. 56, 217–227 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Berkovich, Y.: Subgroups with the character restriction property and related topics. Houston J. Math. 24, 631–638 (1998)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Biró, B., Kiss, E.W., Pálfy, P.P.: On the congruence extension property. Colloq. Math. Soc. Janos Bolyai 29, 129–151 (1982)Google Scholar
  9. 9.
    Bruno, B., Emaldi, M.: On groups all of whose subgroups are normal-sensitive. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 64, 265–269 (1978)MathSciNetGoogle Scholar
  10. 10.
    Kurdachenko, L.A., Otal, J., Subbotin, IYa.: Artinian modules over group rings. Frontiers in Mathematics. Birkhäuser Verlag, Basel (2007)Google Scholar
  11. 11.
    Robinson, D.J.S.: Groups in which normality is a transitive relation. Proc. Camb. Phil. Soc. 60, 21–38 (1964)CrossRefzbMATHGoogle Scholar
  12. 12.
    Robinson, D.J.S.: Sylow permutability in locally finite groups. Ric. Mat. 59, 313–318 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Schmidt, R.: Subgroups lattices of groups. Walter de Gruyter, Berlin (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • Adolfo Ballester-Bolinches
    • 1
  • Leonid A. Kurdachenko
    • 2
  • Javier Otal
    • 3
  • Tatiana Pedraza
    • 4
  1. 1.Departament d’ÀlgebraUniversitat de València Burjassot (València)Spain
  2. 2.Department of AlgebraNational University of DnepropetrovskDnepropetrovskUkraine
  3. 3.Departmento de Matemáticas, IUMAUniversidad de Zaragoza Zaragoza Spain
  4. 4.Instituto Universitario de Matemática Pura y AplicadaUniversidad Politécnica de Valencia ValenciaSpain

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