1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook