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• Abelian group
  Abelian group

  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
  abelian group

  See commutative group

Abelian group

British  

/ 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

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abelian group Scientific  

/ ə-bē′lē-ən /

1. See commutative group

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Etymology

Origin of Abelian group

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

Example Sentences

See Examples For:

Abelian group

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

From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various

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

From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various

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

From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various