Find distinct groups $G$ and $H$ such that each is isomorphic to a proper subgroup of the other Give an example of two groups $G_1$, $ G_2$ such that $G_1$ embed in $G_2 $ and $G_2$ embed in $G_1$ ($H$ embed in $G$ means that there exist $K$ a subgroup of $G$ s.t. $K$ and $H$ are isomorphic), but $$G_1≇G_2.$$ ($G_1≇G_2$ $⟺$ $\nexists f:G_1\to G_2$, $f$ 1-1, onto and homomorphism.)
Thanks in advance. 

Take two free groups of rank 2 and 3.
