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Proving groups are isomorphic

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Recall that given a group G, we defined A(G) to be the set of all isomorphisms from G to itself; you proved that A(G) is a group under composition.
    (a) Prove that A(Zn) is isomorphic to Zn/{0}
    (b) Prove that A(Z) is isomorphic to Z2

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 25, 2009 #2

    Dick

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    There aren't very many automorphisms of Z->Z. In fact, I think there is only two of them. For the other question, I'm not really sure what Z_n/{0} means. Can you explain?
     
  4. Oct 25, 2009 #3
    Can you figure out the sets A(Zn) and A(Z)?
    The identity function is one that should come to mind.
    Take a general function on Z by f(x)=bx for some b in Z. What values can b take on so that f(x) is a bijection?
     
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