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Definition (Kernel Of A Homomorphism)
The kernel of a homomorphism $f:G\to H$ is the set of elements in $G$ that are mapped to the identity $e_H\in H$. In symbols, we'll write the kernel of $f$ as $$\ker(f)=f^{-1}(e_H) = \{g\in G\mid f(g)=e_H\}.$$
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