# Subgroup of abelian normal subgroup

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This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: subgroup and Abelian normal subgroup
View other such compositions|View all subgroup properties
This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: normal subgroup and Abelian normal subgroup
View other such compositions|View all subgroup properties
This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: central subgroup and normal subgroup
View other such compositions|View all subgroup properties

## Definition

### Symbol-free definition

A subgroup of a group is termed a subgroup of Abelian normal subgroup if it satisfies the following equivalent conditions:

1. It is a subgroup of an Abelian normal subgroup.
2. It is a normal subgroup of an Abelian normal subgroup.
3. It is a central subgroup (i.e., it is contained in the center) of a normal subgroup.

### Equivalence of definitions

Further information: equivalence of definitions of subgroup of Abelian normal subgroup