1. The problem statement, all variables and given/known data Prove that the torsion subgroup T of an abelian group G is a normal subgroup of G, and that G/T is torsion free. 2. Relevant equations 3. The attempt at a solution The second part of this exercise makes absolutely no sense to me. We know nothing about G, so why is there any reason that the nonidentity elements of G/T would all have infinite order. G could even be finite. Is the statement of the question correct? Should G be a torsion free group?