Are they isomorphic? $G$ and $G \times G$ where $G = \Bbb Z_2 \times  \Bbb Z_2 \times  \Bbb Z_2 \times\cdots$
The answer says yes but I cannot figure out what homomorphism function I could use.

Think of $$G = \mathbb{Z_{2_1}}\times \mathbb{Z_{2_2}} \times \mathbb{Z_{2_3}} \times \mathbb{Z_{2_4}} \times \mathbb{Z_{2_5}} \times \ldots$$ and $$G \times G= (\mathbb{Z_{2_1}}\times \mathbb{Z_{2_3}} \times \mathbb{Z_{2_5}} \times \ldots) \times (\mathbb{Z_{2_2}}\times \mathbb{Z_{2_4}} \times \mathbb{Z_{2_6}} \times \ldots)$$
