Show that everly element of S(n) (n>=2) is a product of transpositions of the form (k k+1).

[Hint:(k k+2) = (k k+1)(k+1 k+2)(k k+1).]

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- Aug 6th 2007, 10:33 PMr7irisproduct of transpositions
Show that everly element of S(n) (n>=2) is a product of transpositions of the form (k k+1).

[Hint:(k k+2) = (k k+1)(k+1 k+2)(k k+1).] - Aug 7th 2007, 06:03 AMThePerfectHacker
**Theorem:**For every element of can be expressed as a product of transpositions.

Thus, given any premutation we can write it as a product of transpositions and we will show that each of these transpositions is a product of the form .

Say we are working in (products are taken from right to left).

Consider . We can write it as .

Consider . We can write it as .

Consider . We can write it as .

You get the general idea. So that means everything can be expressed in consecutive form by using the theorem.