---
tag: 0PT52XQZD7
kind: concept
name: Product of two subgroups
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Product_of_group_subsets
    locator: lead section
---

## Summary

The product of two subgroups $H$ and $K$ of a group is the set $HK$ of all products $hk$ with $h \in H$ and $k \in K$.
It is a subgroup exactly when $HK = KH$.