Group theory MOC

Abelian group

A group is said to be abelian if all its elements commute. group

Properties

• An abelian group has the same structure as a -module. See Abelian groups as Z-modules.
• An abelian group is equal to its centre, as well as the centraliser of every element.
• Irreps of abelian groups are 1-dimensional
• Kernel of a homomorphism into an abelian group
• All subgroups of an abelian group are normal

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