I am looking for a group $G$ with $\vert G \vert > 1$ which is isomorphic to the direct product $G \times G$.
I have been looking for such a group among non-finite groups, such as $\mathbb{Z}$ or the group of real-valued sequences. However, for these groups, I could not find an isomorphism to the direct products of themselves. Could anyone please give me a hint which particular group might be helpful to consider?