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Math Help - Please Help! A complicated generator question...

  1. #1
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    Please Help! A complicated generator question...

    Suppose that G is a group with less than 1,000,000 elements. Show that you can find no more than 20 elements that generate G.
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  2. #2
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    Quote Originally Posted by iamthemanyes View Post
    Suppose that G is a group with less than 1,000,000 elements. Show that you can find no more than 20 elements that generate G.

    As the minimal order of non-unit element in a group is 2, and as the minimal number of elements a group with 20 generators is \left|\mathbb{Z}_2\times\ldots\times\mathbb{Z}_2\r  ight|=2^{20}>1,000,000 ,

    with 20 direct factors there (why?), then we're done.

    Tonio
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