Let $(G,\cdot)$ and $(H,\times)$ be groups. We say that the function $f:G\to H$ is a group $\textdef{homomorphism}$ if $f(a\cdot b)=f(a)\times f(b)$ for every $a,b\in G$.

• I would like to add something along the lines of “The map is compatible with the group structures of both $G$ and $H$” to the definition above. If someone has a good way of stating this, feel free to add it above.

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• Group homomorphism

definition ben needsreview rben rjosh