group homomorphism

群同态

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

Translation evidence: Literature usage

Meaning in context

A map f:G→Hf:G\to H between groups satisfying f(ab)=f(a)f(b)f(ab)=f(a)f(b) for all a,ba,b.

保持群乘法的群间映射。

Example

det⁡:GL⁡n(F)→F×\det:\operatorname{GL}_n(F)\to F^\times is a homomorphism.

Usage and distinctions

Preservation of identity and inverses follows from the multiplication condition.

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), proposition immediately after the paragraph naming 群同态, multiplication-preservation criterion · 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), proposition immediately after the paragraph naming 群同态, multiplication-preservation criterion · Checked 2026-10-15
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