- #1

- 119

- 0

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?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter gottfried
- Start date

- #1

- 119

- 0

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

- 22,129

- 3,297

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

- 119

- 0

Cool thanks for clearing it up.

Share: