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January 13th, 2009, 02:20 PM   #1
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permutation groups, proof

Can anyone proof that order of even and not even permutation group is n!/2.

danke.
hastalamalejkum
zdravim
thx
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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.
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January 15th, 2009, 08:34 PM   #3
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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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