Mathematics · Group Theory
Which of the following is NOT a valid property or statement regarding the external direct product G1 × G2 of two groups G1 and G2?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(a, b) ∈ G1 × G2 for all a ∈ G1 and b ∈ G2
- 2(e, e') is the identity element of G1 × G2, where e ∈ G1 and e' ∈ G2
- 3If a ∈ G1 and b ∈ G2, then (a, b) ∉ G1 × G2✓
- 4|G1 × G2| = |G1| · |G2| for finite groups
Correct answer
If a ∈ G1 and b ∈ G2, then (a, b) ∉ G1 × G2
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