Torsion Z-modules

An R-module M is called torsion[1] if Tor(M)=M.

  1. Prove that every finite abelian group is torsion as a Z-module.
  2. Give an example of an infinite abelian group that is torsion as a Z-module.

  1. Check here for a reminder of what it means for an element in a module to be torsion. ↩︎