Group Question

1. Nov 9, 2006

Dragonfall

How can I prove the following:

A nonabelian simple group can not operate nontrivially on a set containing fewer than five elements.

I can't get started.

2. Nov 9, 2006

StatusX

When a group acts on a set of n elements, you get a homomorphism from that group into Sn. What can the kernel of this homomorphism be?