So for C6 (cyclic group)
{1,x,x^2,...,x^5}, you can easily determine the generators by just taking the coprime powers. So x and x^5 in this case.
But if I had a composition that was isomorphic to C6 ie:
g1(w) = w
g2(w) = w^2
.
.
.
g6(w) = w^6
What would be the quickest method to find the generators now?
I worked it out (the long way), and the generators are g3(w) = w^3 and g5(w) = w^5. I would have thought, take powers coprime to 6, again, but clearly its not the case, as 3 is not coprime to 6.
Thanks
EDIT: the reason im asking this is because I am currently working on C16 with:
g1(w) = w
g2(w) = w^2
.
.
.
g16(w) = w^16
And you can see, that it would help alot if I knew a trick to find the generators
Thanks
EDIT 2: I think I have found the solution
so gi would be a generator of C16 if i^(16) mod 17 = 1. But I get quite big numbers for this. Ill wait for some more suggestions
EDIT3: Actually my solution is not correct. Because i^16 mod 17 can be 1, but not a generator. Sheesh