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.
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.
The basic idea is that if one selects then one has the -cycle , then selecting one has the -cycle . I think you get the idea now.