Automorphism Groups

  • Thread starter camelite
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  • #1
camelite
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Homework Statement



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

Homework Equations





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)?
 

Answers and Replies

  • #2
matt grime
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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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