411 REFERENCE · Wikibooks
Abstract Algebra/Group Theory/Homomorphism/A Homomorphism with Trivial Kernel is Injective
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Theorem
Let f be a homomorphism from group G to group K.
Let eK be identity of K.
means f is injective.
Proof
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| 0. Choose such that
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| 1.
|| f is a homomorphism
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| 2.
|| 0.
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| 3.
|| f is a homomorphism
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| 4.
|| homomorphism maps identity to identity
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| 5.
|| 1,2,3,4.
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| 6.
|| given
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| 7.
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