---
tag: 0W88CEGQP1
kind: concept
name: Kernel of a homomorphism
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Kernel_(algebra)
    locator: Group homomorphisms
same_as:
  wikidata: Q574844
  wikipedia: Kernel (algebra)
---

## Summary

The kernel of a group homomorphism is the set of elements that it sends to the identity.
It is a normal subgroup, and it measures how far the homomorphism is from being injective.