Abelian group

/əˈbi.li.ən ɡɹup/ noun

noun ·Rare ·Advanced level

Definitions

Noun
  1. 1
    A group in which the group operation is commutative.

    "1986, Partially Ordered Abelian Groups with Interpolation, American Mathematical Society, 2010 softcover reprint, page 12, Let G and H be partially ordered abelian groups. A positive homomorphism from G to H is any abelian group homomorphism f:G→H that maps positive elements to positive elements, that is, f(G⁺)⊆H⁺."

  2. 2
    Alternative letter-case form of abelian group. alt-of
  3. 3
    a group that satisfies the commutative law wordnet

Synonyms

All synonyms
additive groupcommutativecommutative groupcommutative groupcyclic groupfinite additive group

Example

More examples

"1986, Partially Ordered Abelian Groups with Interpolation, American Mathematical Society, 2010 softcover reprint, page 12, Let G and H be partially ordered abelian groups. A positive homomorphism from G to H is any abelian group homomorphism f:G→H that maps positive elements to positive elements, that is, f(G⁺)⊆H⁺."

Etymology

Named in honour of Niels Henrik Abel (1802–1829), a Norwegian mathematician.

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