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Math Help - Permutation

  1. #1
    Junior Member mathemanyak's Avatar
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    Permutation

    Show that Sn={(1,2),(1,2,......,n)}
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Quote Originally Posted by mathemanyak View Post
    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.
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