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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

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

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

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