normal subgroup

正规子群

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

Translation evidence: Literature usage

Meaning in context

A subgroup N≤GN\le G satisfying gNg−1=NgNg^{-1}=N for every g∈Gg\in G.

对群内任意元素的共轭运算都保持不变的子群。

Example

A3A_3 is normal in S3S_3.

Usage and distinctions

Being a subgroup alone does not make multiplication of its cosets well-defined.

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, second paragraph and equation xHx^{-1}=H · 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, second paragraph and equation xHx^{-1}=H · Checked 2026-10-15
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