# Abelianness is quotient-closed

From Groupprops

Revision as of 23:16, 19 May 2011 by Vipul (talk | contribs) (Created page with "{{group metaproperty satisfaction| property = abelian group| metaproperty = quotient-closed group property}} ==Statement== Suppose <math>G</math> is an abelian group and <m...")

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

## Statement

Suppose is an abelian group and is a normal subgroup of . Denote by the quotient group. Then, is also an abelian group.