anonymous
  • anonymous
Prove that if you compose two even permutations, you get an even permutation.
Mathematics
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chestercat
  • chestercat
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watchmath
  • watchmath
even+even=even
anonymous
  • anonymous
permutation formula nPr = n!/(n-r)! where n is total object taken, and r= objects taken at a time proof: nPr =n!/(n-r)! 2P2= 2!/(2-2)! = 2!/0! = 2 where 2 is even
anonymous
  • anonymous
therefore, if you compose two even permutation you'll always get an even answer

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anonymous
  • anonymous
try other given like 4P2 and you will also get an even answer.
watchmath
  • watchmath
I think what he meant by even permutation are the elements in permutation group that can be written as a product of even cycles.
anonymous
  • anonymous
Sorry back, ye what watchmath said, logically it makes sense since you need a even number of transpositions to compose a even permutation, but i wasn't sure of the generic proof.

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