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Need help checking a proof on a cyclic group

  1. Sep 23, 2009 #1
    1. Prove that (Q,+) is not cyclic

    Here is what I have, and I need help knowing if this proof makes sense, is thorough enough, or is completely wrong. Note that (Q,+) is rationals

    Suppose, by contradiction, that (Q,+) is cyclic, p/q E (Q,+) and q=/=0
    => (Q,+) can be generated by <p/q> = {k(p/q)|k E Z}
    if p/(2q) E (Q,+)
    then p/(2q) can be generated by k(p/q)
    => p/(2q)=k(p/q)
    therefore k does not belong to Z and (Q,+) is not cyclic

    It seems like I am missing something or made a conceptual error somewhere. Any help or confirmation is appreciated.
  2. jcsd
  3. Sep 23, 2009 #2


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    Looks good to me
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