Isomorphism $\phi:G\to G\times G$

Question

Can anyone provide me with an example of a non-trivial group $G$ which is isomorphic to $G\times G$. What is the mapping $G \to G\times G$?

Answer 1

Hint : take $G=\mathbb{Z}^{\mathbb{N}}$ and find a bijection from $\mathbb{N}$ onto the union of two copies of $\mathbb{N}$.