abelian group

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see also: Abelian group

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Etymology

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

Pronunciation

• (America) IPA: /əˈbi.li.ən ɡɹup/, /əˈbil.jən ɡɹup/

Noun

abelian group (plural abelian groups)

1. (algebra) 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\rightarrow H that maps positive elements to positive elements, that is, f(G^+)\subseteq H^+.

   • 2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, Softcover reprint of 1st edition, page 74 ↗,

     Chapter 2 is a brief introduction to some fundamental techniques for countable torsion-free abelian groups.

Synonyms

• commutative group

Translations

• French: groupe abélien, groupe commutatif
• German: abelsche Gruppe, kommutative Gruppe
• Italian: gruppo abeliano
• Portuguese: grupo abeliano
• Russian: а́белева гру́ппа
• Spanish: grupo abeliano

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Abelian group

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Noun

abelian group (plural abelian groups)

1. Alternative form of abelian group

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