abelian group

== English == === Alternative forms === Abelian group === Etymology === Named in honour of Niels Henrik Abel (1802–1829), a Norwegian mathematician. === Pronunciation === (US) IPA(key): /əˈbi.li.ən ɡɹup/, /əˈbil.jən ɡɹup/ === Noun === abelian group (plural abelian groups) (algebra) A group in which the group operation is commutative. Synonym: commutative group 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 {\displaystyle f:G\rightarrow H} that maps positive elements to positive elements, that is, f ( G + ) ⊆ H + {\displaystyle 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. ==== Hypernyms ==== group solvable group ==== Hyponyms ==== cyclic group free abelian group torsion subgroup ==== Derived terms ==== free abelian group ==== Translations ==== === Further reading === “abelian group, Abelian group”, in Google Books Ngram Viewer.