abelian group

交换群

Algebra & Algebraic Geometry · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: commutative group · Abel 群

Translation evidence: Literature usage

Meaning in context

A group whose operation satisfies ab=baab=ba for every pair of elements.

任意两个元素的运算次序均可交换的群。

Example

The additive group Z/6Z\mathbb Z/6\mathbb Z is abelian.

Usage and distinctions

Additive notation is conventional, but does not by itself prove commutativity.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. J. S. Milne — Group TheoryChapter 1, Definitions and examples, discussion following Definition 1.1 · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件半群, 幺半群与群，paragraph following def:group naming 交换群 and Abel 群 · Checked 2026-10-14
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