Finding a non- trivial group G such that G is isomorphic to G* G

Question

The question is to find a nontrivial group $G$ such that $G$ is isomorphic to $G\times G$. I cannot find any. First of all if the group is finite then only trivial group is the possible one. So the group cannot be finite. So we need to find among infinite groups. Will anybody please help me in this case.Thanks in advance.

Answer 1

$\mathbb{R}$ and $\mathbb{R} \times \mathbb{R}$ are isomorphic as vector spaces over $\mathbb{Q}$ (They have both an uncountable basis of the same cardinality) so their additive groups are isomorphic.