Group Homomorphism

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Definition (Group Homomorphism)

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

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