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November 25th, 2009, 06:12 AM  #1 
Guest Joined: Posts: n/a Thanks:  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, because 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 
Newbie Joined: Aug 2008 Posts: 10 Thanks: 0  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 2cycles, and knowing that 2cycles and their own inverse will be useful  but it's important to know which 2cycles 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.

November 26th, 2009, 04:50 AM  #3 
Guest Joined: Posts: n/a Thanks:  Re: prove permutation inverse
Thanks.


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