Question Id : 15041 |
Context : UGC NET Computer Science 26 June 2025 (Paper II)
Choose the correct statement for a group G:
🎥 Video solution / Text Solution of this question is given below:
Reason: From (xy)² = xyxy = x²y² = xxyy. Left-multiply by x⁻¹ and right-multiply by y⁻¹ to get yx = xy, hence G is abelian.
(2) and (3) are false (there exist non-abelian groups where every element has order 3 or 5, e.g., unitriangular 3×3 matrices over ℤ₃/ℤ₅).
(4) is false because every subgroup of an abelian (commutative) group is abelian.