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December 3, 2020 2:28 pmpts 30 pts
11. The commutator subgroup of S3 is (A) A (B) S (C)fe) (D) None of these 12. Let H, K be two groups and G = H x K. Then which of the statements i true ? (A) G is solvable Hand K are solvable. (B) Hand K are solvable G is solvable. (C) Both (A) and (B) (D) None of these 13. Let G be a group with at least two elements such that G has no subgroup other than {e} and itself. Then choose the correct statement: (A) G is a cyclic group (B) G is of prime order (C) Both (A) and (B) (D) None of these 14. Which of the following is not a unique factorization domain ? (A) Z-2-{a+ b-2: a,b e Z} (B) Z-=a+b-5:a,b e Z} (C) z2{a+ bN2 : a,b eZ (D) None of these
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