Changes

==Examples==

==Examples==

The symmetric [[Group (Mathematics)|group]] on a set of N points is often written <math>\mathbb{S}_n \ </math> and has <math>n! \ </math> elements.  Each element of a symmetric group is a way of re-arranging the points:  for example, it is possible to re-arrange the points ABCD into so they read BCDA - this is an element of <math>\mathbb{S}_4 \ </math>, and it is written <math>(1432) \ </math>, because the first point went to the fourth position (ie, <math>1 \rightarrow 4 \ </math>), the fourth point went to the third position (ie, <math>4 \rightarrow 3 \ </math>), the third point went to the second position, and the second point went to the first position.

The symmetric [[Group (Mathematics)|group]] on a set of N points is often written <math>\mathbb{S}_n \ </math> and has <math>n! \ </math> elements.  Each element of a symmetric group is a way of re-arranging the points:  for example, it is possible to re-arrange the points ABCD into so they read BCDA - this is an element of <math>\mathbb{S}_4 \ </math>, and it is written <math>(1432) \ </math>, because the first point went to the fourth position (i.e., <math>1 \rightarrow 4 \ </math>), the fourth point went to the third position (i.e., <math>4 \rightarrow 3 \ </math>), the third point went to the second position, and the second point went to the first position.

[[Category:Mathematics]]

[[Category:Mathematics]]

<math>G D E A C F B \ </math>.

<math>G D E A C F B \ </math>.

In this final arrangement, A has ended up at position 4 (ie, <math>1 \rightarrow 4 \ </math>), D has ended up at position 2, and so on, until we discover the product of the two permutations to be <math>(1427)(35) \ </math>.

In this final arrangement, A has ended up at position 4 (i.e., <math>1 \rightarrow 4 \ </math>), D has ended up at position 2, and so on, until we discover the product of the two permutations to be <math>(1427)(35) \ </math>.