If $G$ and $H$ are divisible groups each of which is isomorphic to a subgroup of the other, then $G$ is isomorphic to $H$.
Here, $G$ and $H$ are abelian groups. Can we assume another adjective rather than divisibility?
If $G$ and $H$ are divisible groups each of which is isomorphic to a subgroup of the other, then $G$ is isomorphic to $H$.
Here, $G$ and $H$ are abelian groups. Can we assume another adjective rather than divisibility?