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Infinite Order of Non-Identity Elements

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.
 
Last edited:

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