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Infinite Order of Non-Identity Elements

  1. Feb 14, 2012 #1
    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: Feb 14, 2012
  2. jcsd
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