---
tag: 0S21GNW9ZB
kind: concept
name: Image of a homomorphism
aliases: [range-of-a-homomorphism]
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Group_homomorphism
    locator: Image and kernel
---

## Summary

The image of a group homomorphism $\varphi \colon G \to H$ is the set of the values $\varphi(g)$ for $g \in G$.
It is a subgroup of $H$.