Let G be a finite group with more than one element. Show that G has an element of prime order.

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- Sep 7th 2007, 05:38 PMtttcomraderFinite group with element of prime order
Let G be a finite group with more than one element. Show that G has an element of prime order.

- Sep 7th 2007, 11:49 PMred_dog
Let .

If is prime, we've done.

Else, let be a prime divisor of .

Then .

Let .

Let . Then .

But .

So . - Sep 8th 2007, 04:26 AMtopsquark
- Sep 8th 2007, 05:51 PMThePerfectHacker