Groups with few self-centralizing subgroups which are not self-normalizing

  • Mahmoud Hassanzadeh

    Iran University of Science & Technology, Tehran, Iran
  • Zohreh Mostaghim

    Iran University of Science & Technology, Tehran, Iran
Groups with few self-centralizing subgroups which are not self-normalizing cover

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Abstract

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

DOI 10.4171/RSMUP/30