Group theory MOC

Abelian group

A group is said to be abelian if all its elements commute. #m/def/group

Properties

• An abelian group has the same structure as a -module. See Abelian groups as -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

#state/tidy | #lang/en | #SemBr