Sorry I am not used to using the tex code, but will learn and explain in words for now!(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to prove that for all distinct x and y in a finite set X, there exists a function f in P(X) (the permutation group) such that f(x)=x' and f(y)=y'. Note: x' and y' are also distinct.

I have started by letting P(X) = the symmetry group and have shown that there exists a cycle (x y) which takes two distinct values and returns 2 distinct values. I am pretty sure x can equal y'. Now I am stuck! I have been told that a case-by-case analysis will probably be required. Can somebody point me in the right direction?

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# Homework Help: Permutation Group Proof

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