---
tag: 03DEH43F4H
kind: concept
name: Left coset
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Coset
    locator: Definition
---

## Summary

A left coset of a subgroup $H$ of a group $G$ is a set $gH$, with $g \in G$. You get it when you multiply each element of $H$ on the left by $g$.
The left cosets of $H$ partition $G$.