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The permutation is question is
Solution
Basically, there is more then one way of writing down the elements as products of
transpositions... So (1,3,7) = (1,7) o (1,3) = (4,7) o (1,7) o (1,4) o (1,3) You can see this by
following what happens to the elements in the product:... (4,7) o (1,7) o (1,4) o (1,3) 1 -> 3 3 ->
1 -> 4 -> 7 4 -> 1 -> 7 -> 4 7 -> 1 (remember apply transformations from the back) So you can
see in this product: 1 -> 3 -> 7 -> 1 and 4-> 4 which is the group element (1,3,7)

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The permutation is question isSolution Basic.pdf

  • 1. The permutation is question is Solution Basically, there is more then one way of writing down the elements as products of transpositions... So (1,3,7) = (1,7) o (1,3) = (4,7) o (1,7) o (1,4) o (1,3) You can see this by following what happens to the elements in the product:... (4,7) o (1,7) o (1,4) o (1,3) 1 -> 3 3 -> 1 -> 4 -> 7 4 -> 1 -> 7 -> 4 7 -> 1 (remember apply transformations from the back) So you can see in this product: 1 -> 3 -> 7 -> 1 and 4-> 4 which is the group element (1,3,7)