Thread: Permutation

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

Originally Posted by mathemanyak

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

If then takes j to j+k (mod n) (for j=1,2,...,n). It follows that . But it is well known (see here, for example) that transpositions of adjacent elements generate the whole of S_n.