Is the group (QxQ,+) cyclic?

2 Answers

  • 1 month ago

    Assuming Q is the set of rationals, and the usual definition of + for QxQ, then no.  The denominator of the sum a/b + c/d is always a common multiple of b and d, so you can't add rationals to produce a sum with denominator that's coprime to the denominators of the addends.  So, the group (Q,+) isn't cyclic, and (QxQ,+) can't be cyclic either. There's no way to add copies of (a/b, c/d) to produce (1/p, 1/p), where p is a prime that doesn't divide either b or c.

  • Anonymous
    1 month ago

    Its very simple. I will give you the answer, but you first have to choose my answer as best then I will edit it an put the answer with full working in it.

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