IIT JAM Follow
December 3, 2020 3:21 pm 30 pts
S6. Let G be a group, and let aeG. The function fa: G G defined by Sa(x) = axal Vxe G is called. (A) a homomorphism (B) the inner automorphisSm (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: (A) G and |H| are relatively prime B) G| H (D) None of these (C) G2 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 o G, Z (G) is: ) (B) :a eR (A) (C) :a eR oae (D) None of these