kernel of a group homomorphism

群同态的核

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

Translation evidence: Literature usage

Meaning in context

For f:G→Hf:G\to H, the subgroup {g:f(g)=eH}\{g:f(g)=e_H\}.

群同态中映到目标群单位元的全部元素组成的子群。

Example

Reduction Z→Z/5Z\mathbb Z\to\mathbb Z/5\mathbb Z has kernel 5Z5\mathbb Z.

Usage and distinctions

Use the target identity, not the empty set or an arbitrarily chosen zero.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source同态和商群 (sec:homomorphism), definition of the image and 核 of φ, equation Ker(φ)=φ^{-1}(1) · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件同态和商群 (sec:homomorphism), definition of the image and 核 of φ, equation Ker(φ)=φ^{-1}(1) · Checked 2026-10-15
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