1. The problem statement, all variables and given/known data Show that Z has infinitely many subgroups isomorphic to Z. ( Z is the integers of course ). 2. Relevant equations A subgroup H is isomorphic to Z if [itex]\exists \phi : H → Z[/itex] which is bijective. 3. The attempt at a solution So I didn't really know how to approach this one, I'm guessing I might want to try a proof by contradiction? So I would suppose that Z does not have infinitely many subgroups isomorphic to it. Not quite sure how to start this one.