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Automorphism Groups

  1. Apr 10, 2009 #1
    1. The problem statement, all variables and given/known data

    If G is a finite cyclic group of order n, what is the group Aut(G)? Aut(Aut(G))?

    2. Relevant equations



    3. The attempt at a solution

    Aut(G) is given by the automorphisms that send a generator to a power k < n where (k,n) = 1 with order p(n) where p is Euler's function.

    I'm having trouble visualizing or describing Aut(Aut(G)) as automorphisms of automorphisms. Is Aut(G) isomorphic to a cyclic group of order p(n)?
     
  2. jcsd
  3. Apr 10, 2009 #2

    matt grime

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    Homework Helper

    It is not going to be cyclic in general. You need to try to get a better view of Aut(G).

    You've already identified it as a set as

    { k : 1<=k <n and (k,n)=1}

    What is the group law?
     
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