If φ(7)=7 then φ(7^k)=7^k. So the powers of 7 run through the elements 1,7,19,13, which are half the elements of U(30). Then you have to find what happens to the other 4 elements 11,17,23 and 29. We are told that 11 goes to 1. Then 7*11=17 goes to φ(7)*φ(11)=7, and 7*17=29 goes to φ(7)*φ17)=7*7=19, and 7*29=23 goes to φ(7)*φ(29)=7*19=13.
So the morphism does 1->1, 11->1, 7->7, 17->7, 19->19. 29->19, 13->13, 23->13.
-Linley Johnson --Johns121 17:04, 17 February 2009 (UTC)
Does φ need to be written out as some sort of equation or is it fine to leave it with a map for each element? -Tyler McQueen
