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4.5.1.1: Abelian group

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    An abelian group, also called a commutative group, is a group (G, * ) such that

    \[g_1 * g_2 = g_2 * g_1 \nonumber \]

    for all \(g_1\) and \(g_2\) in \(G\), where \(*\) is a binary operation in \(G\). This means that the order in which the binary operation is performed does not matter, and any two elements of the group commute.

    Groups that are not commutative are called non-abelian (rather than non-commutative).

    Abelian groups are named after Niels Henrik Abel.

    4.5.1.1: Abelian group is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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