Generators of the symmetric group |

each cycle, and hence every element of(i_{1}...i_{r})=(i_{1}i_{2})(i_{2}i_{3}) ...(i_{r-1}i_{r})

Thus the transposition(j,k+1)=(k,k+1)(j,k)(k,k+1).

consisting of theS_{ n}:= { s_{i}:=(i,i+1) | 1 <= i<n }= {(12),(23), ...,(n-1,n) },

so that we have proved(1 ...n)^{i}(12)(1 ...n)^{-i}=(i+1,i+2),1 <= i <= n-2,

Corollary:S_{n}= á(12),(23), ...,(n-1,n) ñ= á(12),(1 ...n) ñ.

harald.fripertinger@kfunigraz.ac.at,

last changed: August 28, 2001

Generators of the symmetric group |