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January 13th, 2009, 02:20 PM  #1 
Newbie Joined: Jan 2009 Posts: 1 Thanks: 0  permutation groups, proof
Can anyone proof that order of even and not even permutation group is n!/2. danke. hastalamalejkum zdravim thx 
January 13th, 2009, 03:53 PM  #2  
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: permutation groups, proof Quote:
Anyway, the even permutations are half of the permutations, and there are n! permutations.  
January 15th, 2009, 08:34 PM  #3 
Member Joined: Jul 2008 From: Minnesota, USA Posts: 52 Thanks: 0  Re: permutation groups, proof
Right, so to prove that the even permutations are half of all the permutations, you create a bijection from the even permutations to the odd permutations. I think that multiplying by (12) [cycle notation] on the right would probably do it. This is assuming you have proven that the parity of transpositions in the factorization of a permutation to transpositions is invariant. Cheers, Nathan 

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