I found this problem, and I was wondering if I'm on the right approach.(adsbygoogle = window.adsbygoogle || []).push({});

Let G be a finite group on a finiste set X with m elelements. Suppose there exist a g[tex]\in[/tex]G and x[tex]\in[/tex]X such that^{g}x not equal to x. Suppose the order of G does not divide m!. Prove that G is not simple.

Would it suffice to show that an isomorphism "f" exists from G to X? Then we just need to prove two cases about the Ker(f). We need to show that Ker(f) can't just be the identity because then it would be an infinite group being isomorphic to a finite group. If the Ker(f)=G, then some stuff. Sorry for the informality, I'm not actually sure what happens if Ker(f)=G.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Group actions

**Physics Forums | Science Articles, Homework Help, Discussion**