Abelian group

/ əˈbiːlɪən /

noun

1. a group the defined binary operation of which is commutative: if a and b are members of an Abelian group then ab = ba

abelian group

1. See commutative group

Word History and Origins

Origin of abelian group¹

C19: named after Niels Henrik Abel (1802–29), Norwegian mathematician

Example Sentences

A group whose operations are all permutable with each other is called an Abelian group.

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An Abelian group contains subgroups whose orders are any given factors of the order of the group.

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In fact, since every subgroup H of an Abelian group G and the corresponding factor groups G/H are Sylow’s theorem.

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