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An important subtype of groups are commutative groups. Therefore, they deserve a separate definition.

Definition: Commutative (Abelian) Group

A commutative group \((G,\ast)\) is a group, in which the binary operation \(\ast\) is commutative, i.e. \(x\ast y=y\ast x\) for all \(x,y\in G\).

A commutative group is also called Abelian, named after Niels Hendrik Abel (1802 – 1829).

“Unfolding” all definitions, an Abelian group fulfills the following axioms:

| | | | | created: 2014-03-22 21:38:36 | modified: 2019-08-04 08:00:41 | by: bookofproofs | references: [577], [6907]

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[6907] Brenner, Prof. Dr. rer. nat., Holger: “Various courses at the University of Osnabrück”, https://de.wikiversity.org/wiki/Wikiversity:Hochschulprogramm, 2014

Bibliography (further reading)

[577] Knauer Ulrich: “Diskrete Strukturen – kurz gefasst”, Spektrum Akademischer Verlag, 2001