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Cyclic automorphism group

  1. Jun 7, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove that no group can have its automorphism group cyclic of odd order.

    2. Relevant equations

    3. The attempt at a solution

    Aut(Z2) has order 1, which is odd...trivial, yes, but I thought I was DONE.

    However, my professor has said "well prove it EXCEPT for Z2"

    I thought I was done, and now I have till 2 to do redo this and I have a mental block on it.

    Can someone give my a push?

  2. jcsd
  3. Jun 7, 2007 #2

    matt grime

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    Homework Helper

    So you've got to show that every group (except Z/2Z) with cyclic aut. grp. has an automorphism of order 2...
  4. Jun 8, 2007 #3
    All right, I think I see it now...although I already turned it in incomplete. I just couldn't see it yesterday.
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