Let G be a finite group such that the automorphism $f:G\to G$ sends more than three quarters of elements of G to their inverses. Show that $f(x)=x^{-1}$ for all $x\in G$ and that $G$ is abelian.
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Did you try to show? – Boris Novikov Jun 27 '13 at 14:44
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I simply didn't get any clue to start with. Please help. – Anupam Jun 27 '13 at 14:45