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Abstract Algebra - Cyclic groups

  1. Oct 26, 2011 #1
    (This is my first post on PF btw - I posted on this another thread, but I'm not sure if I was supposed to)

    I was doing some practice problems for my exam next week and I could not figure this out.

    1. The problem statement, all variables and given/known data

    Suppose a is a group element such that |a^28| = 10 and |a^22| = 20. Determine |a|.

    2. Relevant equations

    Let a be element of order n in group and let k be a positive integer. Then <a^k> = <a^gcd(n,k)> and |a^k| = n/gcd(n,k).

    3. The attempt at a solution

    10 = n/gcd(n, 28); 20 = n/gcd(n, 22)

    Setting n equal to each other, 10gcd(n, 28) = 20gcd(n,22)

    gcd(n, 28) = 2gcd(n, 22)

    The possible values for n are 4, 8, 12, 16, 20, 24, ... , so on.

    Not sure where to go from here.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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