Group Theoretic Version
Given two groups G and H and a group homomorphism f : G→H, let K be a normal subgroup in G and φ the natural surjective homomorphism G→G/K (where G/K is a quotient group). If K is a subset of ker(f) then there exists a unique homomorphism h:G/K→H such that f = h φ.
The situation is described by the following commutative diagram:
By setting K = ker(f) we immediately get the first isomorphism theorem.
Read more about this topic: Fundamental Theorem On Homomorphisms
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