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

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- Aug 7th 2008, 02:24 AMmathemanyakPermutation
Show that Sn={(1,2),(1,2,......,n)}

- Aug 7th 2008, 11:01 AMOpalg
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.