Let G be a finite group and let g G. Let m be the order of g. Prove that in the representation (given by left multiplication) every cycle in the cycle decomposition of the image of g has length m.

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- Sep 30th 2011, 07:39 PMkierkegaardLeft Representation
Let G be a finite group and let g G. Let m be the order of g. Prove that in the representation (given by left multiplication) every cycle in the cycle decomposition of the image of g has length m.

- Sep 30th 2011, 09:14 PMDrexel28Re: Left Representation
- Sep 30th 2011, 09:39 PMDevenoRe: Left Representation
let H = <g>, and be the image of g in the representation. what is the action of on the right cosets Hx?

how is this relevant?