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Math Help - quotient group

  1. #1
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    quotient group

    Consider (\mathbb Q,+) and (\mathbb Q/\mathbb Z,+). Let n\ge1 and define G_n=\left( \left[ \dfrac{a}{n} \right],a\in \mathbb{Z} \right). Prove that G_n is a subgroup of \mathbb Q/\mathbb Z, and that it has order n.

    \left[\dfrac an \right] is the class of \dfrac an.******
    Last edited by hizocar; April 3rd 2011 at 06:48 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by hizocar View Post
    consider the following groups:
    (\mathbb{Q}, +) (\mathbb{Q}/ \mathbb{Z}, +)

    And the group:
    G_{n}=([\frac{a}{n}] / a \in \mathbb{Z})

    proved that Gn is subgroup of Q / Z, and the order of Gn is n.
    This doesn't make much sense, can you rephrase this? Define G_n again...wite it out better.
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  3. #3
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    now?
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  4. #4
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    *****read the first post again, I've edited.******
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  5. #5
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by hizocar View Post
    Consider (\mathbb Q,+) and (\mathbb Q/\mathbb Z,+). Let n\ge1 and define G_n=\left( \left[ \dfrac{a}{n} \right],a\in \mathbb{Z} \right). Prove that G_n is a subgroup of \mathbb Q/\mathbb Z, and that it has order n.

    \left[\dfrac an \right] is the class of \dfrac an.******
    Can you `get' the subgroup bit? For the order bit, I'll give you a hint...

    HINT: \left[\frac{a}{n}\right] = \left[\frac{a+n}{n}\right]
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