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Showing that groups are isomorphic

  1. Oct 11, 2012 #1
    If one wants to show that two groups are isomorphic is simply finding a single isomorphism between them sufficient?

    For example.

    If G is an infinite cyclic group with generator g show that G is isomorphic to [itex]Z[/itex].

    So suppose f(g)=ord(g)

    then f is bijective and a homomorphism I believe?
     
  2. jcsd
  3. Oct 11, 2012 #2

    micromass

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    Yes.

    Yes, this is true. However, you might want to give a bit of explanation on why it is bijective and a homomorphism.
     
  4. Oct 11, 2012 #3
    Cool thanks for clearing it up.
     
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