Mathematics · Abstract Algebra
Choose the correct statement for a group G:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If for all x, y ∈ G, (xy)2 = x2y2, then G is abelian.✓
- 2If for all x ∈ G, x3 = e, then G must be abelian, where e is the identity element.
- 3If for all x ∈ G, x5 = e, then G must be abelian, where e is the identity element.
- 4If G is an abelian group, then any subgroup of G need not be abelian.
Correct answer
If for all x, y ∈ G, (xy)2 = x2y2, then G is abelian.
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