Theorem 14.11

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(The Fundamental Homomorphism Theorem)

Let $\phi : G \rightarrow G'$ be a group homomorphism with kernel $H$. Then $\phi[G]$ is a group, and $\mu : G/H \rightarrow \phi[G]$ given by $\mu(gH) = \phi(g)$ is an isomorphism. If $\gamma : G \rightarrow G/H$ is the homomorphism given by $\gamma(g) = gH$, then $\phi(g) = \mu \gamma(g)$ for each $g \in G$.

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