Showing that groups are isomorphic

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?

Staff Emeritus
Homework Helper
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 $Z$.

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.

gottfried
Cool thanks for clearing it up.