Maybe I'm just making this hard on myself, or maybe I just don't properly understand the definition of cyclic subgroups. My answer just does not match up with the answer in the back of the book. Help would be appreciated.
Thanks!
What I'm getting is <1>, <7>, <11>, <13>, <17>, <19>, <23>, and <29>, but since <7> = <13> and <17> = <23>, the back of the book only lists one of the two. Their choice was to leave out <13> and <23>, but listing <1>, <11>, <13>, <19>, <23>, <29> would be right as well. They simply did not want to list the same subgroup twice. If this is not the issue you were having, let me know and I'll further explain the problem.
