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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
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Re: permutation groups, proof

Quote:
 Originally Posted by MarkyMark Can anyone proof that order of even and not even permutation group is n!/2. danke. hastalamalejkum zdravim thx
"not even permutation group"? The odd permutations are not closed (so not a group).

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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