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First Isomorphism Theorem
Definition: Let f:G -> G' be a surjective group homomorphism with kernel N. The quotient group G/N is isomorphic to the image G'. To be precise, let h: G -> G/N be the canonical map. There is a unique isomorphism F:G/N -> G' such that f=Foh.
Source: Algebra, second edition by Michael Artin