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

## TL;DR

This paper investigates groups where every non-nilpotent subgroup is self-normalizing, providing a complete structural description for soluble and finite perfect groups, and insights into infinite perfect groups.

## Contribution

It characterizes and describes the structure of groups with the property that all non-nilpotent subgroups are self-normalizing, covering soluble, finite perfect, and infinite perfect cases.

## Key findings

- Soluble groups with the property are fully characterized.
- Finite perfect groups with the property are classified.
- Structural information is provided for infinite perfect groups.

## 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.