group

群

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

Translation evidence: Literature usage

Meaning in context

A set with an associative binary operation, an identity, and a two-sided inverse for every element.

配备结合的二元运算、单位元且每个元素都有双侧逆元的集合。

Example

(Z,+)(\mathbb Z,+) has identity 00 and inverse −n-n for nn.

Usage and distinctions

Commutativity is not a group axiom; it defines the additional abelian condition.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. J. S. Milne — Group TheoryChapter 1, Definition 1.1 · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件第四章，半群, 幺半群与群，definition labelled def:group（群） · Checked 2026-10-14
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