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February 16, 2022 1:47 pm 30 pts
For g EZ, let E Z37 denote the residue class of g modulo 37. Consider the group U7 = {ī E Zs7:1sgs37 with ged(g, 37) = 1} with respect to multiplication modulo 37. Then which one of the following is FALSE? options A. There is exactly one group homomorphism from U37 to (Q,+). B. The order of the element 10 in U37 is 36. . The set {g E U37 : = (g)} contains exactly 2 elements. D. There is exactly one group homomorphism from Ua7 to (Z, +).
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• Piyush pachauri
U(37) is isomorphic to Z36 ( cyclic group of order 36) clearly ACD are correct. B is incorrect as 1000 = 1(mod37) so order of 10 is 3 .