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Math Help - Group theory

  1. #1
    Junior Member
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    Group theory

    Prove that <\mathbb Q, +> group has no finite set of generators.

    Any help would be appreciated!
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  2. #2
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
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    For the ease of notation, suppose there are two generators, m_1/n_1, m_2/n_2. Let p be a prime such that \gcd(n_1, n_2,p)=1. Is it possible to write 1/p as a combination of m_1/n_1, m_2/n_2?

    You can generalize this argument for any supposed number of generators.
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