TITLE: Is any transposition a product of simple transpositions?
QUESTION [8 upvotes]: Is any transposition a product of simple transpositions? If yes, how can you prove this?

REPLY [5 votes]: There is an algorithm that takes a permutation and writes it as a product of simple transpositions. It's called bubble sort.
What you do is : if $f(i) > f(i+1)$, write $f$ = $f' \circ (i,i+1)$. Repeat on $f'$ until you get the identity and are left with a product of simple transposition.