More Group Theory

[SaSA :::::]

Let G be a finite group and let f be an element of order 3 in Aut(G), such that f(x)=x, implies x=e. Prove that for every prime factor p of o(G), the p-Sylow subgroup of G is normal in G. This is problem 19 in section 2.12 of Herstein's topics in algebra. I tried showing that f maps N(P) to G, but I don't really know if or how it can be done.

[Sourayan Banerjee]

Give a read to these first

1) Group Action

2) Frobenius group action and its kernel.

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