# Showing that groups are isomorphic

1. Oct 11, 2012

### gottfried

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 $Z$.

So suppose f(g)=ord(g)

then f is bijective and a homomorphism I believe?

2. Oct 11, 2012

### micromass

Staff Emeritus
Yes.

Yes, this is true. However, you might want to give a bit of explanation on why it is bijective and a homomorphism.

3. Oct 11, 2012

### gottfried

Cool thanks for clearing it up.