The problem says show that U(20) does not equal <k> for any k in U(20). [Hence U(20) is not cyclic.] I was trying to understand Example 1 from the Chapter 3 in the text book. where it discusses U(15). I am completely confused about what it is talking about:
U(15) = {1, 2, 4, 7, 8, 11, 13, 14 } Then it goes on to say to find the order of element 7, so |7| = 4 $ 7^1 = 7space 7^2 =4 space 7^3 = 13 7^4 = 1 $
