Monatshefte für Mathematik

, Volume 185, Issue 4, pp 591–600 | Cite as

Groups in which every non-abelian subgroup is self-normalizing

  • Costantino Delizia
  • Urban Jezernik
  • Primož Moravec
  • Chiara Nicotera


We study groups having the property that every non-abelian subgroup is equal to its normalizer. This class of groups is closely related to an open problem posed by Berkovich. We give a full classification of finite groups having the above property. We also describe all infinite soluble groups in this class.


Normalizer Non-abelian subgroup Self-normalizing subgroup 

Mathematics Subject Classification

20E34 20D15 20E32 


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Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  1. 1.University of SalernoFiscianoItaly
  2. 2.University of LjubljanaLjubljanaSlovenia

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