# Cocentral subgroup of normalizer

From Groupprops

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

This is a variation of cocentral subgroup|Find other variations of cocentral subgroup |

## Contents

## Definition

### Symbol-free definition

A subgroup of a group is said to be a **cocentral subgroup of normalizer** if it is a cocentral subgroup of its normalizer.

### Definition with symbols

A subgroup of a group is said to be a **cocentral subgroup of normalizer** if where denotes the center of and denotes the normalizer of .

## Formalisms

### In terms of the in-normalizer operator

This property is obtained by applying the in-normalizer operator to the property: cocentral subgroup

View other properties obtained by applying the in-normalizer operator

## Relation with other properties

### Stronger properties

### Weaker properties

## Metaproperties

### Trimness

This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself).

View other trim subgroup properties | View other trivially true subgroup properties | View other identity-true subgroup properties