quotient group

商群

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

Translation evidence: Literature usage

Meaning in context

For a normal subgroup NN of GG, the group of cosets with (gN)(hN)=ghN(gN)(hN)=ghN.

对正规子群 NN，由陪集构成并以代表元乘法诱导运算的群。

Example

Z/4Z\mathbb Z/4\mathbb Z is an additive quotient group.

Usage and distinctions

For a nonnormal subgroup the coset set exists but this multiplication need not.

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 headed 商群, normal-subgroup hypothesis and coset multiplication · 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 headed 商群, normal-subgroup hypothesis and coset multiplication · Checked 2026-10-15
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