# Abelianness is subgroup-closed

From Groupprops

This article gives the statement, and possibly proof, of a group property (i.e., abelian group) satisfying a group metaproperty (i.e., subgroup-closed group property)

View all group metaproperty satisfactions | View all group metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for group properties

Get more facts about abelian group |Get facts that use property satisfaction of abelian group | Get facts that use property satisfaction of abelian group|Get more facts about subgroup-closed group property

## Contents

## Statement

Any subgroup of an abelian group is an abelian group.

## Related facts

### Related nice properties of abelian groups

- Abelianness is varietal
- Abelianness is quotient-closed
- Abelianness is direct product-closed
- Abelianness is 2-local