# Abnormal normalizer not implies pronormal

From Groupprops

This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., subgroup with abnormal normalizer) neednotsatisfy the second subgroup property (i.e., pronormal subgroup)

View a complete list of subgroup property non-implications | View a complete list of subgroup property implications

Get more facts about subgroup with abnormal normalizer|Get more facts about pronormal subgroup

EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property subgroup with abnormal normalizer but not pronormal subgroup|View examples of subgroups satisfying property subgroup with abnormal normalizer and pronormal subgroup

## Statement

A subgroup whose normalizer is an abnormal subgroup need not be pronormal.

## Facts used

## Proof

The proof follows directly by combining facts (1) and (2).