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

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- September 7th 2007, 04:38 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.

- September 7th 2007, 10:49 PMred_dog
Let .

If is prime, we've done.

Else, let be a prime divisor of .

Then .

Let .

Let . Then .

But .

So . - September 8th 2007, 03:26 AMtopsquark
- September 8th 2007, 04:51 PMThePerfectHacker