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Math Help - Fixed Point free automorphism of order 3

  1. #1
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    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.


    Please email me in case you have a solution on chandru.mcc@gmail.com...


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  2. #2
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    Quote Originally Posted by Chandru1 View Post
    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.
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