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Math Help - factor group question

  1. #1
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    factor group question

    Let G be an Abelian group and let H be the subgroup consisting of all elements of G that have finite order. Prove that every non-identity element in G/H has infinite order.
    No clue were to go, or even start from. Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by wutang View Post
    Let G be an Abelian group and let H be the subgroup consisting of all elements of G that have finite order. Prove that every non-identity element in G/H has infinite order.
    No clue were to go, or even start from. Any help would be appreciated.

    gH\in G\slash H has finite order \Longrightarrow g^nH=H\Longrightarrow g^n\in H , for some n\in\mathbb{N}\Longrightarrow g has finite order and thus...

    Tonio
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  3. #3
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    so I assume that their exists an element gH in G/H that has finite order to get a contradiction? I still do not understand it fully.
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  4. #4
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    Quote Originally Posted by wutang View Post
    so I assume that their exists an element gH in G/H that has finite order to get a contradiction? I still do not understand it fully.

    What I wrote actually means: if an element has finite order in G\slash H then that element must be the unit element, and thus...well, and thus exactly what

    you want to prove, right?

    Tonio
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