Mathematics · Abstract Algebra
Which of the following statements is TRUE for any group G?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If G is commutative, then any subgroup of G need not be commutative.
- 2If the order of G is prime, then G cannot be commutative.
- 3If for all x ∈ G, x2 = 1, then G is commutative, where 1 is the identity element of G.✓
- 4If for all x, y ∈ G, (xy)2 = x2y2, then G must be non-commutative.
Correct answer
If for all x ∈ G, x2 = 1, then G is commutative, where 1 is the identity element of G.
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