I do not understand how to tell what a generator of a subgroup is? I think that the subgroups of Z20 are (1,2,4,5,10,20), but that also might not be right. Anyways I could use a little explanation please.
Check the back of the book. Theres a selected answer/hint section. It gives some good information about the problem. The subgroups are given by (1,2,4,5,10,20), which are the generators. So I think you are on the right track. Hope that helps.