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Let N1 be a normal subgroup of group G1, and N2 be a normal subgroup of...

Let N1 be a normal subgroup of group G1, and N2 be a normal subgroup of group G2. Use the Fundamental Homomorphism Theorem to show that

G1/N1 × G2/N2 ≃ (G1 × G2)/(N1 × N2).

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