Groups in which every non-abelian subgroup is self-normalized
  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. 
Costantino Delizia, Urban Jezernik, Primoz Moravec, Chiara Nicotera
math.GR