# Nilpotent Hall subgroup

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: Hall subgroup with a group property (itself viewed as a subgroup property): nilpotent group

View a complete list of such conjunctions

## Contents

## Definition

A subgroup of a finite group is termed a **nilpotent Hall subgroup** if it is a Hall subgroup (i.e., its order and index are relatively prime) and also a nilpotent group.

## Relation with other properties

### Stronger properties

### Weaker properties

- Isomorph-conjugate Hall subgroup
- Isomorph-conjugate subgroup:
`For full proof, refer: Nilpotent Hall implies isomorph-conjugate` - Intermediately isomorph-conjugate subgroup
- Pronormal Hall subgroup:
`For full proof, refer: Nilpotent Hall implies pronormal` - Procharacteristic subgroup
- Pronormal subgroup:
`For full proof, refer: Nilpotent Hall implies pronormal`