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kernel

For a homomorphism $f: G \to H$ , the set $\ker(f) = \{g \in G : f(g) = e_H\}$ -- always a normal subgroup of $G$ .

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Examples

For $f:\mathbb{Z}_6\to\mathbb{Z}_3$ , $f(x)=x\bmod 3$ , the kernel is $\{0,3\}$ .