Mathematics · Group Theory
Let G1 and G2 be subgroups of a group G. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If G1 is a normal subgroup of G, then (G2G1)/G1 ≅ G2/(G2 ∩ G1) is false.
- 2Every subgroup of prime index in G is normal.
- 3If G1 is normal in G2 and G2 is normal in G, then G1 must be normal in G.✓
- 4If H1 and H2 are normal subgroups of G1 and G2 respectively, then (G1 × G2)/(H1 × H2) ≅ (G1/H1) × (G2/H2).
Correct answer
If G1 is normal in G2 and G2 is normal in G, then G1 must be normal in G.
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