1. The problem statement, all variables and given/known data G is an abelian group with H the subgroup of elements of G with finite order. Prove that every non-identity element in G/H has infinite order. 2. Relevant equations 3. The attempt at a solution Suppose gH in G/H has order n. Then (gH)n = gnH so gn is in H. Then there is some m > 0 such that gnm = e. So g is in H. At this point, I am stuck - I do not know how to show that g must be the identity element. EDIT: Figured it out.