Abelian groups

Overview

Abelian group

A group $G$ is abelian if the group operation commutes, meaning $ab=ba$ for all $a,b\in G$.

Related notes:

• Free abelian group
• Group generators, relations, and presentations
• Commutator subgroups and abelianization

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Properties

• Normal subgroups and quotient groups: Every subgroup of an abelian group is normal.

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Examples

Group of homomorphism between abelian groups

If