Please Help! A complicated generator question...

May 2010
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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.
 
Oct 2009
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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 \(\displaystyle \left|\mathbb{Z}_2\times\ldots\times\mathbb{Z}_2\right|=2^{20}>1,000,000\) ,

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

Tonio
 
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