11. the commutator subgroup of s3 is (a) as (b) s3 (c) {e) (d) none of these 12. let h, k be two groups and g = h x k. then which of the statements is true ? (a

11. The commutator subgroup of S3 is (A) As (B) S3 (C) {e) (D) None of these 12. Let H, K be two groups and G = H x K. Then which of the statements is true ? (A) G is solvable H and K are solvable. (B) H and 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) z2-{a+bN-2:a,b e Z} (B) Z5= {a + b-5 :a,b e Z} (C) z2=a+ b2: a, b e Z (D) None of these TIC (4)