- #1

gottfried

- 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?

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- Thread starter gottfried
- Start date

- #1

gottfried

- 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

- 22,178

- 3,305

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

- 119

- 0

Cool thanks for clearing it up.

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