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## Lemma: Kernel and Image of a Group Homomorphism are Subgroups

Let $$f:(G,\ast)\mapsto (H,\cdot)$$ a group homomorphism. Then it follows that

1. The kernel $$\ker(f)$$ is a subgroup of $$G$$.
2. The image $$\operatorname{im}(f)$$ is a subgroup of $$H$$.

| | | | | created: 2014-09-06 16:20:51 | modified: 2019-07-27 15:56:06 | by: bookofproofs | references: [696]