# Math Help - Permutation

1. ## Permutation

Show that Sn={(1,2),(1,2,......,n)}

2. Originally Posted by mathemanyak
Show that Sn={(1,2),(1,2,......,n)}
If $\sigma = (1,2,\ldots,n)$ then $\sigma^k$ takes j to j+k (mod n) (for j=1,2,...,n). It follows that $\sigma^{k-1}(1,2)\sigma^{-k+1} = (k,k+1)$. But it is well known (see here, for example) that transpositions of adjacent elements generate the whole of S_n.