I've been working on a problem and I can't seem to figure out as to why the book wants you to use Lagrange's theorem. The question is "Prove that if k is an integer that is relatively prime to the order of a finite group, then the map x --> x^k is surjective." My idea was that since n and k are relatively prime, then ns + kt = 1 so that x = x^(ns+kt) which simplifies to x = x^(ks) so that x is the image of x^s and it is surjective. So where does Lagrange's theorem come into play?(adsbygoogle = window.adsbygoogle || []).push({});

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# Why the need for Lagrange's Theorem?

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