# Math Help - Fixed Point free automorphism of order 3

1. ## Fixed Point free automorphism of order 3

Let G be a finite group, φ an automorphism of G such that φ3 is the identity automorphism. Suppose further that φ(x)=x if and only if x=e. Prove that for every prime p which divides o(G) the p-Sylow subgroup is normal in G.

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Thanks

2. Originally Posted by Chandru1
Please email me in case you have a solution on chandru.mcc@gmail.com...
what?!!

Let G be a finite group, φ an automorphism of G such that φ3 is the identity automorphism. Suppose further that φ(x)=x if and only if x=e. Prove that for every prime p which divides o(G) the p-Sylow subgroup is normal in G.
read chapter 10 of the book "Finite Groups" written by "Daniel Gorenstein" for a solution to your problem and also if you want to learn more about fixed-point free automorphisms of a finite group.