1. The problem statement, all variables and given/known data Let a be an element of a group an let |a| = 15. Compute the orders of the following elements of G a) a^3, a^6, a^9, a^12 2. Relevant equations 3. The attempt at a solution for the first part of part a, would a^3 be <a^3>=<e,a^3,a^6,a^9,a^12,a^15,a^18,a^21,a^24,a^27,a^30, a^33,a^36,a^39,a^42>
|a|=15 means that 15 is the lowest power of a that is equal to the identity. So, for example, [tex]a^{42}=a^{15}\times a^{15} \times a^{12}=e \times e \times a^{12}=a^{12}[/tex] so you've got too many things in your list.
What I want to know is why the OP stopped after a^42 in particular. I mean going beyond a^15 is clearly wrong, but why stop at a^42? Is that the 15th power of a^3? I think so, from quickly scanning the list.