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Let phi: G1 -> G2 be a surjective group homomorphism. Let H1 be a normal subgroup...

Let phi: G1 -> G2 be a surjective group homomorphism. Let H1 be a normal subgroup of G1 and suppose that phi(H1) = H2. Disprove that G1/H1 G2/H2. Hint: find a counterexample where phi is not injective.

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