---
tag: 0KYX2N69J0
kind: concept
name: Quotient group
aliases: [factor-group]
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Quotient_group
    locator: Definition
same_as:
  wikidata: Q1138961
  wikipedia: Quotient group
---

## Summary

The quotient group $G/N$ of a group $G$ by a normal subgroup $N$ is the set of cosets of $N$, with the product $(aN)(bN) = abN$.
It collapses $N$ to the identity and keeps the rest of the structure of $G$.