# Maximal among abelian normal subgroups

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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]

## Definition

### Symbol-free definition

A subgroup of a group is termed maximal among Abelian normal subgroups if it is an Abelian normal subgroup and there is no Abelian normal subgroup properly containing it.

### Definition with symbols

A subgroup $H$ of a group $G$ is termed maximal among Abelian normal subgroups if $H$ is an Abelian normal subgroup of $G$, and for any $K$ containing $H$ that is an Abelian normal subgroup of $G$, $H = K$.

## Formalisms

### In terms of the maximal operator

This property is obtained by applying the maximal operator to the property: Abelian normal subgroup
View other properties obtained by applying the maximal operator