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

/ ə-bē′lē-ən /

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.

From Project Gutenberg

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

From Project Gutenberg

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

From Project Gutenberg