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

2017/05/17 by Delizia, C., Jezernik, U., Moravec, P. +1
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1705.06265

Abstract

We study the class of groups having the property that every non-nilpotent subgroup is equal to its normalizer. These groups are either soluble or perfect. We completely describe the structure of soluble groups and finite perfect groups with the above property. Furthermore, we give some structural information in the infinite perfect case.

Related

• Groups in which every non-abelian subgroup is self-normalized
• On non self-normalizing subgroups
• Abelian Carter subgroups in finite permutation groups
• A note on groups with self-normalizing cyclic subgroups
• Finite groups with many normalizers