IIT JAM Follow
December 3, 2020 2:41 pm 30 pts
56. Let G be be a group, and let a e G. The function fa Sax) = axal Vx e G is called a:GG defined by (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 e His cyclic ifft: (A) G| and |H| are relatively prime (B) G H (C)G 2 H (D) None of these The units of the integral domain of Gaussian integers are : 59 (B) ti (A) t1 (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: (8) :a eR a 0 (D) None of these (C) :acR
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