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Computing the order of a group 
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#1
Sep607, 08:42 AM

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 <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> 


#2
Sep607, 09:11 AM

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P: 2,538

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. 


#3
Sep607, 01:33 PM

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P: 9,396

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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