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Cyclic Automorphism Group

  1. Oct 18, 2006 #1
    I came accross a section of my notes that claimed the automorphism group of the cyclec groups C_2p where p=5,7,11 is cyclic,
    that is Aut(C_2p) is cyclic for p = 5,7,11.
    I wasn't able to see why this is so.
    Is it just a fact or is there some sort of proof of the above...?
    Thanks
     
  2. jcsd
  3. Oct 18, 2006 #2

    matt grime

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    What is the automorphism group of the cyclic group? It sends a generator to a primitive power of itself. I.e. in C_m with generated g, any aut sends g to g^m for some m with (m,n)=1. You can work it out from there.
     
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