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

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