Archiv der Mathematik

, Volume 109, Issue 4, pp 305–310 | Cite as

Normalisers of residuals of finite groups

  • A. Ballester-BolinchesEmail author
  • S. F. Kamornikov
  • H. Meng


Let \(\mathfrak {F}\) be a subgroup-closed saturated formation of finite groups containing all finite nilpotent groups, and let M be a subgroup of a finite group G normalising the \(\mathfrak {F}\)-residual of every non-subnormal subgroup of G. We show that M normalises the \(\mathfrak {F}\)-residual of every subgroup of G. This answers a question posed by Gong and Isaacs (Arch Math 108:1–7, 2017) when \(\mathfrak {F}\) is the formation of all finite supersoluble groups.


Finite group Formation Residual Subnormality 

Mathematics Subject Classification

20D10 20D35 


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    L. Gong and I. M. Isaacs, Normalizers of nilpotent residuals, Arch. Math. 108 (2017), 1–7.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • A. Ballester-Bolinches
    • 1
    Email author
  • S. F. Kamornikov
    • 2
  • H. Meng
    • 1
  1. 1.Departament de MatemàtiquesUniversitat de ValènciaBurjassotSpain
  2. 2.Department of MathematicsFrancisk Skorina Gomel State UniversityGomelBelarus

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