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  1. #1
    Senior Member Danneedshelp's Avatar
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    subgroup question

    Q: Find all possible finite subgroups of the non negative rational numbers under multiplication.

    I can only think of the singleton set containing the identity element which would be of order 1. All other sets would be of infinite order. I feel there is more to this though.

    thanks
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  2. #2
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    Quote Originally Posted by Danneedshelp View Post
    Q: Find all possible finite subgroups of the non negative rational numbers under multiplication.

    I can only think of the singleton set containing the identity element which would be of order 1. All other sets would be of infinite order. I feel there is more to this though.

    thanks

    The non-negative rationals under multiplication are not a group...the POSITIVE rationals are, though.

    As for your solution it is correct: if 0<q\in\mathbb{Q}\,,\,\,then\,\,\{q^n\}_{n=1}^\inft  y is an infinite set...

    Tonio
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  3. #3
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by tonio View Post
    The non-negative rationals under multiplication are not a group...the POSITIVE rationals are, though.

    As for your solution it is correct: if 0<q\in\mathbb{Q}\,,\,\,then\,\,\{q^n\}_{n=1}^\inft  y is an infinite set...

    Tonio
    Is it supposed to be 1\ne q\in\mathbb{Q} instead of 0<q\in\mathbb{Q}?

    Edit: Meh I was thinking of \,\mathbb{Q} as the positive rationals, should have rewritten the set or instead restricted q\not\in\{-1,0,1\}.
    Last edited by undefined; September 18th 2010 at 07:51 PM.
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  4. #4
    Senior Member Danneedshelp's Avatar
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    Quote Originally Posted by tonio View Post
    The non-negative rationals under multiplication are not a group...the POSITIVE rationals are, though.

    As for your solution it is correct: if 0<q\in\mathbb{Q}\,,\,\,then\,\,\{q^n\}_{n=1}^\inft  y is an infinite set...

    Tonio

    Oh, my bad. I don't know why I wrote that.

    Should it be for all q\in{\mathbb{Q}}-\{0\} and q\neq\\e?

    Thanks for the help
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    Quote Originally Posted by Danneedshelp View Post
    Oh, my bad. I don't know why I wrote that.

    Should it be for all q\in{\mathbb{Q}}-\{0\} and q\neq\\e?

    Thanks for the help


    Yes, but it is also true for the positive rationals only (without 1)
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