# computing the order of a group

by Benzoate
Tags: computing, order
 P: 569 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 =
 Sci Advisor HW Helper P: 2,535 |a|=15 means that 15 is the lowest power of a that is equal to the identity. So, for example, $$a^{42}=a^{15}\times a^{15} \times a^{12}=e \times e \times a^{12}=a^{12}$$ so you've got too many things in your list.
 Sci Advisor HW Helper P: 9,398 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.

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