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November 25th, 2009, 06:12 AM   #1

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prove permutation inverse

This should be rather straight forward, but I thought I would ask for some inout from those better an group theory than me.

Let . Prove that

What would be a good way to go about this?. I am just learning some group theory and thought this was a good problem involving cycles.

I was thinking Let , where Then,


and keep going until we get to e. I have more, but it is too much Latexing with all those sigmas
November 25th, 2009, 08:26 AM   #2
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Re: prove permutation inverse

To start with , holds for all bijections (not just permutations -- on the other hand it holds for all groups, either way works). Splitting any cycle into a product of 2-cycles, and knowing that 2-cycles and their own inverse will be useful -- but it's important to know which 2-cycles a cycle is split into. You should be able to prove the theorem just using these three facts: If so, then it's worth going back to prove those lemmas.
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November 26th, 2009, 04:50 AM   #3

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Re: prove permutation inverse


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inverse, permutation, prove

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