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**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}= g

^{n}H so g

^{n}is in H.

Then there is some m > 0 such that g

^{nm}= 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.

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