Showing that groups are isomorphic

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  • #1
gottfried
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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?
 

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  • #2
micromass
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If one wants to show that two groups are isomorphic is simply finding a single isomorphism between them sufficient?

Yes.

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?

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

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