A subscription is required to access this article.
A self-normalizing subgroup is always self-centralizing, but the converse is not necessarily true. Given a finite group , we denote by the number of all self-centralizing subgroups of which are not self-normalizing. We observe that if and only if is abelian, and that if is nonabelian nilpotent then . We also prove that if then is solvable. Finally, we provide structural information in the case when .
Cite this article
Mahmoud Hassanzadeh, Zohreh Mostaghim, Groups with few self-centralizing subgroups which are not self-normalizing. Rend. Sem. Mat. Univ. Padova 142 (2019), pp. 69–80