# Subgroup with abnormal normalizer

From Groupprops

This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: normal subgroup and abnormal subgroup

View other such compositions|View all subgroup properties

## Contents

## Definition

A **subgroup with abnormal normalizer** is a subgroup in a group whose normalizer is an abnormal subgroup.

## Relation with other properties

### Stronger properties

- Abnormal subgroup
- Pronormal subgroup:
*For proof of the implication, refer Normalizer of pronormal implies abnormal and for proof of its strictness (i.e. the reverse implication being false) refer Abnormal normalizer not implies pronormal*. - Characteristic subgroup of pronormal subgroup