1. The problem statement, all variables and given/known data Find a normal subgroup H of Zmn of order m where m and n are positive integers. Show that H is isomorphic to Zm. 2. Relevant equations 3. The attempt at a solution I am honestly not even sure where to start. My initial thoughts were if Zmn was isomorphic to Zm x Zn then I could find a subgroup H from that group. However, I discovered that Zmn is isomorphic to Zm x Zn but the converse is not true. Any help would be appreciated. Edit: If Zmn is cyclic has an element of order mn say x. Then nx has order m. Let H=⟨nx⟩. Now I just need to show that H is isomorphic to Zm, by constructing an isomorphism.