Abelian group

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noun

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

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

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Examples have not been reviewed.

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

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