# Thread: Please Help! A complicated generator question...

1. ## 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.

2. Originally Posted by iamthemanyes
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