Ciro Santilli
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Group homomorphism | 🗖 nosplit | ↑ parent "Group isomorphism" | 93, 2, 118

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Like isomorphism, but does not have to be one-to-one: multiple different inputs can have the same output.
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The image is as for any function smaller or equal in size as the domain of course.
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This brings us to the key intuition about group homomorphisms: they are a way to split out a larger group into smaller groups that retains a subset of the original structure.
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As shown by the fundamental theorem on homomorphisms, each group homomorphism is fully characterized by a normal subgroup of the domain.
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