IIT JAM Follow
December 3, 2020 3:30 pm 30 pts
56. Let G be a group, and let a e G. The function f: G G defined by Sa x)= axal Vx e G is called (A) a homomorphism (B) the inner automorphism (C) an isomorphism (D) None of these 57. Which of the following is not true? (A) Every field is a division ring. (B) Every division ring is a field. (C) Every commutative division ring is a field. (D) None of these 58. Let G and H be finite cyclic groups. Then G His cyclic iff: (B) IG| H (A) |G and |H| are relatively prime (D) None of these (C) G 2 |H 59. The units of the integral domain of Gaussian integers are: (B) ti (A) +1 (D) None of these (C) Both (A) and (B) 60. Let G be the group of all 2 x 2 non-singular matrices over the reals. Then center of G, Z (G) is ( (A) (B) :aeR a 0) a 0 (D) None of these (C) :a eR a