Mathematics · Group Theory
Let G be a group. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Every subgroup of prime index in G is normal in G.
- 2If H1 is normal in H2 and H2 is normal in G, then H1 is normal in G.
- 3If N1 and N2 are normal subgroups of G1 and G2 respectively, then (G1 × G2) / (N1 × N2) ≅ (G1 / N1) × (G2 / N2).✓
- 4If H1 is a normal subgroup of G and H2 is any subgroup of G, then H1 ∩ H2 is normal in G.
Correct answer
If N1 and N2 are normal subgroups of G1 and G2 respectively, then (G1 × G2) / (N1 × N2) ≅ (G1 / N1) × (G2 / N2).
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