Question

For an abelian group G, let tG = {x E G: x has finite order} denote...

For an abelian group G, let tG = {x E G: x has finite order} denote its torsion subgroup.

  1. Show that t defines a functor Ab -> Ab if one defines t(f) = f|tG (f restricted on tG) for every homomorphism f.
  2. If f is injective, then t(f) is injective.
  3. Give an example of a surjective homomorphism f for which t(f) is not surjective.
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