subgroup

子群

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

Translation evidence: Literature usage

Meaning in context

A subset $H$ of a group $G$ containing the identity and closed under multiplication and inverses.

包含群的单位元且对乘法和取逆均封闭的子集。

Example

$2\mathbb Z$ is a subgroup of $(\mathbb Z,+)$.

Usage and distinctions

A nonempty subset closed only under multiplication need not be a subgroup for infinite groups.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source半群, 幺半群与群 (sec:group-and-monoid), definition headed 子群和正规子群, first paragraph defining subgroup closure and identity · Checked 2026-10-15

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 (sec:group-and-monoid), definition headed 子群和正规子群, first paragraph defining subgroup closure and identity · Checked 2026-10-15

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